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

Percentage Accurate: 79.5% → 88.7%

Time: 14.8s

Alternatives: 13

Speedup: 0.7×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 88.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-272}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c))))
   (if (<= t_1 -5e-272)
     (/ (+ b (- (* x (* 9.0 y)) (* (* z 4.0) (* t a)))) (* z c))
     (if (<= t_1 0.0)
       (/ (+ (* -4.0 (/ (* a (* z t)) c)) (+ (* 9.0 (/ (* x y) c)) (/ b c))) z)
       (if (<= t_1 INFINITY) t_1 (* a (/ (* t -4.0) c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double tmp;
	if (t_1 <= -5e-272) {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c);
	} else if (t_1 <= 0.0) {
		tmp = ((-4.0 * ((a * (z * t)) / c)) + ((9.0 * ((x * y) / c)) + (b / c))) / z;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = a * ((t * -4.0) / c);
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double tmp;
	if (t_1 <= -5e-272) {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c);
	} else if (t_1 <= 0.0) {
		tmp = ((-4.0 * ((a * (z * t)) / c)) + ((9.0 * ((x * y) / c)) + (b / c))) / z;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = a * ((t * -4.0) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)
	tmp = 0
	if t_1 <= -5e-272:
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c)
	elif t_1 <= 0.0:
		tmp = ((-4.0 * ((a * (z * t)) / c)) + ((9.0 * ((x * y) / c)) + (b / c))) / z
	elif t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = a * ((t * -4.0) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -5e-272)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(t * a)))) / Float64(z * c));
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(-4.0 * Float64(Float64(a * Float64(z * t)) / c)) + Float64(Float64(9.0 * Float64(Float64(x * y) / c)) + Float64(b / c))) / z);
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(Float64(t * -4.0) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	tmp = 0.0;
	if (t_1 <= -5e-272)
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c);
	elseif (t_1 <= 0.0)
		tmp = ((-4.0 * ((a * (z * t)) / c)) + ((9.0 * ((x * y) / c)) + (b / c))) / z;
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = a * ((t * -4.0) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(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]}, If[LessEqual[t$95$1, -5e-272], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(N[(-4.0 * N[(N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$1, N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -4.99999999999999982e-272

   1. Initial program 89.7%

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

      1. +-commutative 89.7%

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

      2. associate-+r- 89.7%

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

      3. *-commutative 89.7%

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

      4. associate-*r* 92.7%

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

      5. *-commutative 92.7%

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

      6. associate-+r- 92.7%

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

      7. +-commutative 92.7%

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

      8. associate-*l* 92.7%

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

      9. associate-*l* 92.1%

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

      10. *-commutative 92.1%

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

   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. Add Preprocessing

   if -4.99999999999999982e-272 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -0.0

   1. Initial program 39.0%

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

   3. Simplified 38.0%

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

   5. Taylor expanded in z around 0 99.8%

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

   if -0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 90.1%

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

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c))

   1. Initial program 0.0%

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

   3. Simplified 0.6%

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

   5. Taylor expanded in t around inf 57.4%

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

      1. *-commutative 57.4%

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

      2. associate-/l* 83.6%

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

      3. associate-*r* 83.6%

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

      4. *-commutative 83.6%

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

      5. *-commutative 83.6%

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

      6. associate-*l/ 83.6%

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

   7. Simplified 83.6%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -5 \cdot 10^{-272}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c} + \left(9 \cdot \frac{x \cdot y}{c} + \frac{b}{c}\right)}{z}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-272}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c} + \frac{b}{c}}{z}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c))))
   (if (<= t_1 -5e-272)
     (/ (+ b (- (* x (* 9.0 y)) (* (* z 4.0) (* t a)))) (* z c))
     (if (<= t_1 0.0)
       (/ (+ (* -4.0 (/ (* a (* z t)) c)) (/ b c)) z)
       (if (<= t_1 INFINITY) t_1 (* a (/ (* t -4.0) c)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double tmp;
	if (t_1 <= -5e-272) {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c);
	} else if (t_1 <= 0.0) {
		tmp = ((-4.0 * ((a * (z * t)) / c)) + (b / c)) / z;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = a * ((t * -4.0) / c);
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double tmp;
	if (t_1 <= -5e-272) {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c);
	} else if (t_1 <= 0.0) {
		tmp = ((-4.0 * ((a * (z * t)) / c)) + (b / c)) / z;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = a * ((t * -4.0) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)
	tmp = 0
	if t_1 <= -5e-272:
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c)
	elif t_1 <= 0.0:
		tmp = ((-4.0 * ((a * (z * t)) / c)) + (b / c)) / z
	elif t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = a * ((t * -4.0) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= -5e-272)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(t * a)))) / Float64(z * c));
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(-4.0 * Float64(Float64(a * Float64(z * t)) / c)) + Float64(b / c)) / z);
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(Float64(t * -4.0) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	tmp = 0.0;
	if (t_1 <= -5e-272)
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c);
	elseif (t_1 <= 0.0)
		tmp = ((-4.0 * ((a * (z * t)) / c)) + (b / c)) / z;
	elseif (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = a * ((t * -4.0) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(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]}, If[LessEqual[t$95$1, -5e-272], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(N[(-4.0 * N[(N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$1, N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -4.99999999999999982e-272

   1. Initial program 89.7%

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

      1. +-commutative 89.7%

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

      2. associate-+r- 89.7%

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

      3. *-commutative 89.7%

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

      4. associate-*r* 92.7%

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

      5. *-commutative 92.7%

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

      6. associate-+r- 92.7%

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

      7. +-commutative 92.7%

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

      8. associate-*l* 92.7%

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

      9. associate-*l* 92.1%

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

      10. *-commutative 92.1%

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

   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. Add Preprocessing

   if -4.99999999999999982e-272 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < -0.0

   1. Initial program 39.0%

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

   3. Simplified 38.0%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in x around 0 89.8%

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

   if -0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 90.1%

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

   if +inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x #s(literal 9 binary64)) y) (*.f64 (*.f64 (*.f64 z #s(literal 4 binary64)) t) a)) b) (*.f64 z c))

   1. Initial program 0.0%

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

   3. Simplified 0.6%

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

   5. Taylor expanded in t around inf 57.4%

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

      1. *-commutative 57.4%

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

      2. associate-/l* 83.6%

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

      3. associate-*r* 83.6%

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

      4. *-commutative 83.6%

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

      5. *-commutative 83.6%

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

      6. associate-*l/ 83.6%

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

   7. Simplified 83.6%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -5 \cdot 10^{-272}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{-4 \cdot \frac{a \cdot \left(z \cdot t\right)}{c} + \frac{b}{c}}{z}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := a \cdot \frac{t \cdot -4}{c}\\ \mathbf{if}\;y \leq -9 \cdot 10^{-113}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} \cdot \frac{9}{c}\right)\\ \mathbf{elif}\;y \leq -1.38 \cdot 10^{-269}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-121}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+22}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (/ (* t -4.0) c))))
   (if (<= y -9e-113)
     (* x (* (/ y z) (/ 9.0 c)))
     (if (<= y -1.38e-269)
       t_1
       (if (<= y 6.4e-121)
         (/ (/ b z) c)
         (if (<= y 6.5e-17)
           t_1
           (if (<= y 1.9e+22) (/ b (* z c)) (* 9.0 (* (/ y c) (/ x z))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * ((t * -4.0) / c);
	double tmp;
	if (y <= -9e-113) {
		tmp = x * ((y / z) * (9.0 / c));
	} else if (y <= -1.38e-269) {
		tmp = t_1;
	} else if (y <= 6.4e-121) {
		tmp = (b / z) / c;
	} else if (y <= 6.5e-17) {
		tmp = t_1;
	} else if (y <= 1.9e+22) {
		tmp = b / (z * c);
	} else {
		tmp = 9.0 * ((y / c) * (x / z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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 = a * ((t * (-4.0d0)) / c)
    if (y <= (-9d-113)) then
        tmp = x * ((y / z) * (9.0d0 / c))
    else if (y <= (-1.38d-269)) then
        tmp = t_1
    else if (y <= 6.4d-121) then
        tmp = (b / z) / c
    else if (y <= 6.5d-17) then
        tmp = t_1
    else if (y <= 1.9d+22) then
        tmp = b / (z * c)
    else
        tmp = 9.0d0 * ((y / c) * (x / z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * ((t * -4.0) / c);
	double tmp;
	if (y <= -9e-113) {
		tmp = x * ((y / z) * (9.0 / c));
	} else if (y <= -1.38e-269) {
		tmp = t_1;
	} else if (y <= 6.4e-121) {
		tmp = (b / z) / c;
	} else if (y <= 6.5e-17) {
		tmp = t_1;
	} else if (y <= 1.9e+22) {
		tmp = b / (z * c);
	} else {
		tmp = 9.0 * ((y / c) * (x / z));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = a * ((t * -4.0) / c)
	tmp = 0
	if y <= -9e-113:
		tmp = x * ((y / z) * (9.0 / c))
	elif y <= -1.38e-269:
		tmp = t_1
	elif y <= 6.4e-121:
		tmp = (b / z) / c
	elif y <= 6.5e-17:
		tmp = t_1
	elif y <= 1.9e+22:
		tmp = b / (z * c)
	else:
		tmp = 9.0 * ((y / c) * (x / z))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(Float64(t * -4.0) / c))
	tmp = 0.0
	if (y <= -9e-113)
		tmp = Float64(x * Float64(Float64(y / z) * Float64(9.0 / c)));
	elseif (y <= -1.38e-269)
		tmp = t_1;
	elseif (y <= 6.4e-121)
		tmp = Float64(Float64(b / z) / c);
	elseif (y <= 6.5e-17)
		tmp = t_1;
	elseif (y <= 1.9e+22)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * ((t * -4.0) / c);
	tmp = 0.0;
	if (y <= -9e-113)
		tmp = x * ((y / z) * (9.0 / c));
	elseif (y <= -1.38e-269)
		tmp = t_1;
	elseif (y <= 6.4e-121)
		tmp = (b / z) / c;
	elseif (y <= 6.5e-17)
		tmp = t_1;
	elseif (y <= 1.9e+22)
		tmp = b / (z * c);
	else
		tmp = 9.0 * ((y / c) * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e-113], N[(x * N[(N[(y / z), $MachinePrecision] * N[(9.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.38e-269], t$95$1, If[LessEqual[y, 6.4e-121], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[y, 6.5e-17], t$95$1, If[LessEqual[y, 1.9e+22], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -9.0000000000000002e-113

   1. Initial program 77.4%

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

   3. Simplified 79.7%

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

   5. Taylor expanded in t around 0 59.1%

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

      1. +-commutative 59.1%

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

      2. *-commutative 59.1%

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

   7. Simplified 59.1%

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

   8. Taylor expanded in x around inf 41.5%

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

      1. associate-*r/ 41.5%

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

      2. *-commutative 41.5%

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

      3. *-commutative 41.5%

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

      4. times-frac 39.4%

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

      5. associate-*r/ 41.5%

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

      6. associate-*l* 42.5%

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

   10. Simplified 42.5%

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

   if -9.0000000000000002e-113 < y < -1.38000000000000008e-269 or 6.40000000000000038e-121 < y < 6.4999999999999996e-17

   1. Initial program 79.4%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in t around inf 47.5%

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

      1. *-commutative 47.5%

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

      2. associate-/l* 55.4%

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

      3. associate-*r* 55.4%

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

      4. *-commutative 55.4%

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

      5. *-commutative 55.4%

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

      6. associate-*l/ 55.4%

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

   7. Simplified 55.4%

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

   if -1.38000000000000008e-269 < y < 6.40000000000000038e-121

   1. Initial program 88.8%

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

   3. Simplified 86.2%

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

   6. Applied egg-rr 47.9%

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

   7. Taylor expanded in b around inf 51.3%

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

      1. associate-*r/ 57.2%

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

   9. Applied egg-rr 57.2%

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

   10. Taylor expanded in z around 0 57.4%

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

   if 6.4999999999999996e-17 < y < 1.9000000000000002e22

   1. Initial program 99.8%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in b around inf 86.1%

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

      1. *-commutative 86.1%

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

   7. Simplified 86.1%

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

   if 1.9000000000000002e22 < y

   1. Initial program 76.1%

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

   3. Simplified 74.7%

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

   5. Taylor expanded in x around inf 57.7%

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

      1. *-commutative 57.7%

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

      2. *-commutative 57.7%

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

      3. *-commutative 57.7%

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

      4. times-frac 64.3%

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

   7. Simplified 64.3%

      \[\leadsto \color{blue}{9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 4: 50.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := a \cdot \frac{t \cdot -4}{c}\\ \mathbf{if}\;y \leq -9 \cdot 10^{-113}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-269}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-121}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+23}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (/ (* t -4.0) c))))
   (if (<= y -9e-113)
     (* 9.0 (* x (/ y (* z c))))
     (if (<= y -1.35e-269)
       t_1
       (if (<= y 6.2e-121)
         (/ (/ b z) c)
         (if (<= y 4.4e-20)
           t_1
           (if (<= y 5.4e+23) (/ b (* z c)) (* 9.0 (* (/ y c) (/ x z))))))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * ((t * -4.0) / c);
	double tmp;
	if (y <= -9e-113) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else if (y <= -1.35e-269) {
		tmp = t_1;
	} else if (y <= 6.2e-121) {
		tmp = (b / z) / c;
	} else if (y <= 4.4e-20) {
		tmp = t_1;
	} else if (y <= 5.4e+23) {
		tmp = b / (z * c);
	} else {
		tmp = 9.0 * ((y / c) * (x / z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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 = a * ((t * (-4.0d0)) / c)
    if (y <= (-9d-113)) then
        tmp = 9.0d0 * (x * (y / (z * c)))
    else if (y <= (-1.35d-269)) then
        tmp = t_1
    else if (y <= 6.2d-121) then
        tmp = (b / z) / c
    else if (y <= 4.4d-20) then
        tmp = t_1
    else if (y <= 5.4d+23) then
        tmp = b / (z * c)
    else
        tmp = 9.0d0 * ((y / c) * (x / z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * ((t * -4.0) / c);
	double tmp;
	if (y <= -9e-113) {
		tmp = 9.0 * (x * (y / (z * c)));
	} else if (y <= -1.35e-269) {
		tmp = t_1;
	} else if (y <= 6.2e-121) {
		tmp = (b / z) / c;
	} else if (y <= 4.4e-20) {
		tmp = t_1;
	} else if (y <= 5.4e+23) {
		tmp = b / (z * c);
	} else {
		tmp = 9.0 * ((y / c) * (x / z));
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = a * ((t * -4.0) / c)
	tmp = 0
	if y <= -9e-113:
		tmp = 9.0 * (x * (y / (z * c)))
	elif y <= -1.35e-269:
		tmp = t_1
	elif y <= 6.2e-121:
		tmp = (b / z) / c
	elif y <= 4.4e-20:
		tmp = t_1
	elif y <= 5.4e+23:
		tmp = b / (z * c)
	else:
		tmp = 9.0 * ((y / c) * (x / z))
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(Float64(t * -4.0) / c))
	tmp = 0.0
	if (y <= -9e-113)
		tmp = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))));
	elseif (y <= -1.35e-269)
		tmp = t_1;
	elseif (y <= 6.2e-121)
		tmp = Float64(Float64(b / z) / c);
	elseif (y <= 4.4e-20)
		tmp = t_1;
	elseif (y <= 5.4e+23)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * ((t * -4.0) / c);
	tmp = 0.0;
	if (y <= -9e-113)
		tmp = 9.0 * (x * (y / (z * c)));
	elseif (y <= -1.35e-269)
		tmp = t_1;
	elseif (y <= 6.2e-121)
		tmp = (b / z) / c;
	elseif (y <= 4.4e-20)
		tmp = t_1;
	elseif (y <= 5.4e+23)
		tmp = b / (z * c);
	else
		tmp = 9.0 * ((y / c) * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e-113], N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.35e-269], t$95$1, If[LessEqual[y, 6.2e-121], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[y, 4.4e-20], t$95$1, If[LessEqual[y, 5.4e+23], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -9.0000000000000002e-113

   1. Initial program 77.4%

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

   3. Simplified 79.7%

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

   5. Taylor expanded in x around inf 41.5%

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

      1. associate-/l* 43.5%

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

      2. *-commutative 43.5%

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

   7. Simplified 43.5%

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

   if -9.0000000000000002e-113 < y < -1.35000000000000008e-269 or 6.1999999999999997e-121 < y < 4.39999999999999982e-20

   1. Initial program 79.4%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in t around inf 47.5%

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

      1. *-commutative 47.5%

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

      2. associate-/l* 55.4%

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

      3. associate-*r* 55.4%

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

      4. *-commutative 55.4%

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

      5. *-commutative 55.4%

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

      6. associate-*l/ 55.4%

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

   7. Simplified 55.4%

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

   if -1.35000000000000008e-269 < y < 6.1999999999999997e-121

   1. Initial program 88.8%

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

   3. Simplified 86.2%

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

   6. Applied egg-rr 47.9%

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

   7. Taylor expanded in b around inf 51.3%

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

      1. associate-*r/ 57.2%

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

   9. Applied egg-rr 57.2%

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

   10. Taylor expanded in z around 0 57.4%

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

   if 4.39999999999999982e-20 < y < 5.3999999999999997e23

   1. Initial program 99.8%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in b around inf 86.1%

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

      1. *-commutative 86.1%

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

   7. Simplified 86.1%

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

   if 5.3999999999999997e23 < y

   1. Initial program 76.1%

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

   3. Simplified 74.7%

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

   5. Taylor expanded in x around inf 57.7%

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

      1. *-commutative 57.7%

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

      2. *-commutative 57.7%

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

      3. *-commutative 57.7%

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

      4. times-frac 64.3%

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

   7. Simplified 64.3%

      \[\leadsto \color{blue}{9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 5: 49.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} t_1 := a \cdot \frac{t \cdot -4}{c}\\ t_2 := 9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{-113}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{-269}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-117}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+15}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (/ (* t -4.0) c))) (t_2 (* 9.0 (* x (/ y (* z c))))))
   (if (<= y -9e-113)
     t_2
     (if (<= y -9.6e-269)
       t_1
       (if (<= y 1.9e-117)
         (/ (/ b z) c)
         (if (<= y 9.5e-20) t_1 (if (<= y 1.55e+15) (/ b (* z c)) t_2)))))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * ((t * -4.0) / c);
	double t_2 = 9.0 * (x * (y / (z * c)));
	double tmp;
	if (y <= -9e-113) {
		tmp = t_2;
	} else if (y <= -9.6e-269) {
		tmp = t_1;
	} else if (y <= 1.9e-117) {
		tmp = (b / z) / c;
	} else if (y <= 9.5e-20) {
		tmp = t_1;
	} else if (y <= 1.55e+15) {
		tmp = b / (z * c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((t * (-4.0d0)) / c)
    t_2 = 9.0d0 * (x * (y / (z * c)))
    if (y <= (-9d-113)) then
        tmp = t_2
    else if (y <= (-9.6d-269)) then
        tmp = t_1
    else if (y <= 1.9d-117) then
        tmp = (b / z) / c
    else if (y <= 9.5d-20) then
        tmp = t_1
    else if (y <= 1.55d+15) then
        tmp = b / (z * c)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * ((t * -4.0) / c);
	double t_2 = 9.0 * (x * (y / (z * c)));
	double tmp;
	if (y <= -9e-113) {
		tmp = t_2;
	} else if (y <= -9.6e-269) {
		tmp = t_1;
	} else if (y <= 1.9e-117) {
		tmp = (b / z) / c;
	} else if (y <= 9.5e-20) {
		tmp = t_1;
	} else if (y <= 1.55e+15) {
		tmp = b / (z * c);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	t_1 = a * ((t * -4.0) / c)
	t_2 = 9.0 * (x * (y / (z * c)))
	tmp = 0
	if y <= -9e-113:
		tmp = t_2
	elif y <= -9.6e-269:
		tmp = t_1
	elif y <= 1.9e-117:
		tmp = (b / z) / c
	elif y <= 9.5e-20:
		tmp = t_1
	elif y <= 1.55e+15:
		tmp = b / (z * c)
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(Float64(t * -4.0) / c))
	t_2 = Float64(9.0 * Float64(x * Float64(y / Float64(z * c))))
	tmp = 0.0
	if (y <= -9e-113)
		tmp = t_2;
	elseif (y <= -9.6e-269)
		tmp = t_1;
	elseif (y <= 1.9e-117)
		tmp = Float64(Float64(b / z) / c);
	elseif (y <= 9.5e-20)
		tmp = t_1;
	elseif (y <= 1.55e+15)
		tmp = Float64(b / Float64(z * c));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * ((t * -4.0) / c);
	t_2 = 9.0 * (x * (y / (z * c)));
	tmp = 0.0;
	if (y <= -9e-113)
		tmp = t_2;
	elseif (y <= -9.6e-269)
		tmp = t_1;
	elseif (y <= 1.9e-117)
		tmp = (b / z) / c;
	elseif (y <= 9.5e-20)
		tmp = t_1;
	elseif (y <= 1.55e+15)
		tmp = b / (z * c);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(x * N[(y / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e-113], t$95$2, If[LessEqual[y, -9.6e-269], t$95$1, If[LessEqual[y, 1.9e-117], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[y, 9.5e-20], t$95$1, If[LessEqual[y, 1.55e+15], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.0000000000000002e-113 or 1.55e15 < y

   1. Initial program 76.8%

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

   3. Simplified 77.5%

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

   5. Taylor expanded in x around inf 48.6%

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

      1. associate-/l* 51.0%

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

      2. *-commutative 51.0%

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

   7. Simplified 51.0%

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

   if -9.0000000000000002e-113 < y < -9.6000000000000004e-269 or 1.89999999999999986e-117 < y < 9.5e-20

   1. Initial program 79.4%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in t around inf 47.5%

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

      1. *-commutative 47.5%

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

      2. associate-/l* 55.4%

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

      3. associate-*r* 55.4%

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

      4. *-commutative 55.4%

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

      5. *-commutative 55.4%

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

      6. associate-*l/ 55.4%

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

   7. Simplified 55.4%

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

   if -9.6000000000000004e-269 < y < 1.89999999999999986e-117

   1. Initial program 88.8%

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

   3. Simplified 86.2%

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

   6. Applied egg-rr 47.9%

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

   7. Taylor expanded in b around inf 51.3%

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

      1. associate-*r/ 57.2%

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

   9. Applied egg-rr 57.2%

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

   10. Taylor expanded in z around 0 57.4%

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

   if 9.5e-20 < y < 1.55e15

   1. Initial program 99.8%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in b around inf 86.1%

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

      1. *-commutative 86.1%

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

   7. Simplified 86.1%

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

Alternative 6: 82.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+167}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+205}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -8e+167)
   (* t (/ (* a -4.0) c))
   (if (<= z 7.8e+205)
     (/ (+ b (- (* x (* 9.0 y)) (* (* z 4.0) (* t a)))) (* z c))
     (* a (/ (* t -4.0) c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -8e+167) {
		tmp = t * ((a * -4.0) / c);
	} else if (z <= 7.8e+205) {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c);
	} else {
		tmp = a * ((t * -4.0) / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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 <= (-8d+167)) then
        tmp = t * ((a * (-4.0d0)) / c)
    else if (z <= 7.8d+205) then
        tmp = (b + ((x * (9.0d0 * y)) - ((z * 4.0d0) * (t * a)))) / (z * c)
    else
        tmp = a * ((t * (-4.0d0)) / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -8e+167) {
		tmp = t * ((a * -4.0) / c);
	} else if (z <= 7.8e+205) {
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c);
	} else {
		tmp = a * ((t * -4.0) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if z <= -8e+167:
		tmp = t * ((a * -4.0) / c)
	elif z <= 7.8e+205:
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c)
	else:
		tmp = a * ((t * -4.0) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -8e+167)
		tmp = Float64(t * Float64(Float64(a * -4.0) / c));
	elseif (z <= 7.8e+205)
		tmp = Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(t * a)))) / Float64(z * c));
	else
		tmp = Float64(a * Float64(Float64(t * -4.0) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (z <= -8e+167)
		tmp = t * ((a * -4.0) / c);
	elseif (z <= 7.8e+205)
		tmp = (b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / (z * c);
	else
		tmp = a * ((t * -4.0) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -8e+167], N[(t * N[(N[(a * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e+205], N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.0000000000000003e167

   1. Initial program 39.3%

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

   3. Simplified 47.4%

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

   5. Taylor expanded in z around 0 50.1%

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

   6. Taylor expanded in a around inf 62.8%

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

      1. associate-*r/ 62.8%

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

      2. associate-*r* 63.4%

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

      3. associate-*l/ 70.4%

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

      4. *-commutative 70.4%

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

   8. Simplified 70.4%

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

   if -8.0000000000000003e167 < z < 7.7999999999999997e205

   1. Initial program 87.6%

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

      1. +-commutative 87.6%

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

      2. associate-+r- 87.6%

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

      3. *-commutative 87.6%

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

      4. associate-*r* 87.1%

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

      5. *-commutative 87.1%

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

      6. associate-+r- 87.1%

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

      7. +-commutative 87.1%

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

      8. associate-*l* 87.1%

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

      9. associate-*l* 85.8%

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

      10. *-commutative 85.8%

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

   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. Add Preprocessing

   if 7.7999999999999997e205 < z

   1. Initial program 42.9%

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

   3. Simplified 37.1%

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

   5. Taylor expanded in t around inf 77.9%

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

      1. *-commutative 77.9%

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

      2. associate-/l* 77.5%

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

      3. associate-*r* 77.5%

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

      4. *-commutative 77.5%

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

      5. *-commutative 77.5%

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

      6. associate-*l/ 77.5%

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

   7. Simplified 77.5%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+167}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+205}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+129}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-123}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1.5e+129)
   (* a (/ (* t -4.0) c))
   (if (<= t 1.6e-123)
     (/ (+ b (* 9.0 (* x y))) (* z c))
     (* t (/ (* a -4.0) c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.5e+129) {
		tmp = a * ((t * -4.0) / c);
	} else if (t <= 1.6e-123) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = t * ((a * -4.0) / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-1.5d+129)) then
        tmp = a * ((t * (-4.0d0)) / c)
    else if (t <= 1.6d-123) then
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    else
        tmp = t * ((a * (-4.0d0)) / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.5e+129) {
		tmp = a * ((t * -4.0) / c);
	} else if (t <= 1.6e-123) {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	} else {
		tmp = t * ((a * -4.0) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -1.5e+129:
		tmp = a * ((t * -4.0) / c)
	elif t <= 1.6e-123:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	else:
		tmp = t * ((a * -4.0) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -1.5e+129)
		tmp = Float64(a * Float64(Float64(t * -4.0) / c));
	elseif (t <= 1.6e-123)
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	else
		tmp = Float64(t * Float64(Float64(a * -4.0) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -1.5e+129)
		tmp = a * ((t * -4.0) / c);
	elseif (t <= 1.6e-123)
		tmp = (b + (9.0 * (x * y))) / (z * c);
	else
		tmp = t * ((a * -4.0) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -1.5e+129], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e-123], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(a * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.50000000000000015e129

   1. Initial program 64.6%

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

   3. Simplified 70.1%

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

   5. Taylor expanded in t around inf 64.9%

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

      1. *-commutative 64.9%

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

      2. associate-/l* 72.8%

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

      3. associate-*r* 72.8%

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

      4. *-commutative 72.8%

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

      5. *-commutative 72.8%

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

      6. associate-*l/ 72.8%

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

   7. Simplified 72.8%

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

   if -1.50000000000000015e129 < t < 1.59999999999999989e-123

   1. Initial program 85.1%

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

   3. Simplified 83.5%

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

   5. Taylor expanded in t around 0 76.7%

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

      1. +-commutative 76.7%

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

      2. *-commutative 76.7%

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

   7. Simplified 76.7%

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

   if 1.59999999999999989e-123 < t

   1. Initial program 79.0%

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

   3. Simplified 79.1%

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

   5. Taylor expanded in z around 0 75.2%

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

   6. Taylor expanded in a around inf 48.0%

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

      1. associate-*r/ 48.0%

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

      2. associate-*r* 48.1%

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

      3. associate-*l/ 56.7%

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

      4. *-commutative 56.7%

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

   8. Simplified 56.7%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+129}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-123}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.58 \cdot 10^{+49} \lor \neg \left(t \leq 1.26 \cdot 10^{-123}\right):\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -1.58e+49) (not (<= t 1.26e-123)))
   (* a (/ (* t -4.0) c))
   (* b (/ (/ 1.0 z) c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -1.58e+49) || !(t <= 1.26e-123)) {
		tmp = a * ((t * -4.0) / c);
	} else {
		tmp = b * ((1.0 / z) / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((t <= (-1.58d+49)) .or. (.not. (t <= 1.26d-123))) then
        tmp = a * ((t * (-4.0d0)) / c)
    else
        tmp = b * ((1.0d0 / z) / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -1.58e+49) || !(t <= 1.26e-123)) {
		tmp = a * ((t * -4.0) / c);
	} else {
		tmp = b * ((1.0 / z) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -1.58e+49) or not (t <= 1.26e-123):
		tmp = a * ((t * -4.0) / c)
	else:
		tmp = b * ((1.0 / z) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -1.58e+49) || !(t <= 1.26e-123))
		tmp = Float64(a * Float64(Float64(t * -4.0) / c));
	else
		tmp = Float64(b * Float64(Float64(1.0 / z) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -1.58e+49) || ~((t <= 1.26e-123)))
		tmp = a * ((t * -4.0) / c);
	else
		tmp = b * ((1.0 / z) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -1.58e+49], N[Not[LessEqual[t, 1.26e-123]], $MachinePrecision]], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(1.0 / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.57999999999999992e49 or 1.26000000000000005e-123 < t

   1. Initial program 75.5%

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

   3. Simplified 77.5%

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

   5. Taylor expanded in t around inf 51.1%

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

      1. *-commutative 51.1%

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

      2. associate-/l* 60.6%

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

      3. associate-*r* 60.6%

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

      4. *-commutative 60.6%

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

      5. *-commutative 60.6%

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

      6. associate-*l/ 60.7%

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

   7. Simplified 60.7%

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

   if -1.57999999999999992e49 < t < 1.26000000000000005e-123

   1. Initial program 86.0%

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

   3. Simplified 83.2%

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

   5. Taylor expanded in b around inf 48.5%

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

      1. *-commutative 48.5%

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

   7. Simplified 48.5%

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

      1. div-inv 48.5%

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

   9. Applied egg-rr 48.5%

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

   10. Taylor expanded in z around 0 48.5%

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

       1. *-commutative 48.5%

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

       2. associate-/r* 50.1%

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

   12. Simplified 50.1%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.58 \cdot 10^{+49} \lor \neg \left(t \leq 1.26 \cdot 10^{-123}\right):\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+49} \lor \neg \left(t \leq 1.4 \cdot 10^{-123}\right):\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -3.4e+49) (not (<= t 1.4e-123)))
   (* a (/ (* t -4.0) c))
   (/ b (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -3.4e+49) || !(t <= 1.4e-123)) {
		tmp = a * ((t * -4.0) / c);
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((t <= (-3.4d+49)) .or. (.not. (t <= 1.4d-123))) then
        tmp = a * ((t * (-4.0d0)) / c)
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -3.4e+49) || !(t <= 1.4e-123)) {
		tmp = a * ((t * -4.0) / c);
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -3.4e+49) or not (t <= 1.4e-123):
		tmp = a * ((t * -4.0) / c)
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -3.4e+49) || !(t <= 1.4e-123))
		tmp = Float64(a * Float64(Float64(t * -4.0) / c));
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -3.4e+49) || ~((t <= 1.4e-123)))
		tmp = a * ((t * -4.0) / c);
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -3.4e+49], N[Not[LessEqual[t, 1.4e-123]], $MachinePrecision]], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.4000000000000001e49 or 1.3999999999999999e-123 < t

   1. Initial program 75.5%

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

   3. Simplified 77.5%

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

   5. Taylor expanded in t around inf 51.1%

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

      1. *-commutative 51.1%

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

      2. associate-/l* 60.6%

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

      3. associate-*r* 60.6%

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

      4. *-commutative 60.6%

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

      5. *-commutative 60.6%

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

      6. associate-*l/ 60.7%

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

   7. Simplified 60.7%

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

   if -3.4000000000000001e49 < t < 1.3999999999999999e-123

   1. Initial program 86.0%

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

   3. Simplified 83.2%

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

   5. Taylor expanded in b around inf 48.5%

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

      1. *-commutative 48.5%

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

   7. Simplified 48.5%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+49} \lor \neg \left(t \leq 1.4 \cdot 10^{-123}\right):\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 46.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.05 \cdot 10^{+49} \lor \neg \left(t \leq 4.6 \cdot 10^{-124}\right):\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -3.05e+49) (not (<= t 4.6e-124)))
   (* -4.0 (/ (* t a) c))
   (/ b (* z c))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -3.05e+49) || !(t <= 4.6e-124)) {
		tmp = -4.0 * ((t * a) / c);
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((t <= (-3.05d+49)) .or. (.not. (t <= 4.6d-124))) then
        tmp = (-4.0d0) * ((t * a) / c)
    else
        tmp = b / (z * c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -3.05e+49) || !(t <= 4.6e-124)) {
		tmp = -4.0 * ((t * a) / c);
	} else {
		tmp = b / (z * c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -3.05e+49) or not (t <= 4.6e-124):
		tmp = -4.0 * ((t * a) / c)
	else:
		tmp = b / (z * c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -3.05e+49) || !(t <= 4.6e-124))
		tmp = Float64(-4.0 * Float64(Float64(t * a) / c));
	else
		tmp = Float64(b / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -3.05e+49) || ~((t <= 4.6e-124)))
		tmp = -4.0 * ((t * a) / c);
	else
		tmp = b / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -3.05e+49], N[Not[LessEqual[t, 4.6e-124]], $MachinePrecision]], N[(-4.0 * N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.04999999999999982e49 or 4.60000000000000024e-124 < t

   1. Initial program 75.5%

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

   3. Simplified 77.5%

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

   5. Taylor expanded in t around inf 51.1%

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

   if -3.04999999999999982e49 < t < 4.60000000000000024e-124

   1. Initial program 86.0%

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

   3. Simplified 83.2%

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

   5. Taylor expanded in b around inf 48.5%

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

      1. *-commutative 48.5%

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

   7. Simplified 48.5%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.05 \cdot 10^{+49} \lor \neg \left(t \leq 4.6 \cdot 10^{-124}\right):\\ \;\;\;\;-4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-123}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1.3e+49)
   (* a (/ (* t -4.0) c))
   (if (<= t 1.6e-123) (* b (/ (/ 1.0 z) c)) (* t (/ (* a -4.0) c)))))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.3e+49) {
		tmp = a * ((t * -4.0) / c);
	} else if (t <= 1.6e-123) {
		tmp = b * ((1.0 / z) / c);
	} else {
		tmp = t * ((a * -4.0) / c);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-1.3d+49)) then
        tmp = a * ((t * (-4.0d0)) / c)
    else if (t <= 1.6d-123) then
        tmp = b * ((1.0d0 / z) / c)
    else
        tmp = t * ((a * (-4.0d0)) / c)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.3e+49) {
		tmp = a * ((t * -4.0) / c);
	} else if (t <= 1.6e-123) {
		tmp = b * ((1.0 / z) / c);
	} else {
		tmp = t * ((a * -4.0) / c);
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -1.3e+49:
		tmp = a * ((t * -4.0) / c)
	elif t <= 1.6e-123:
		tmp = b * ((1.0 / z) / c)
	else:
		tmp = t * ((a * -4.0) / c)
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -1.3e+49)
		tmp = Float64(a * Float64(Float64(t * -4.0) / c));
	elseif (t <= 1.6e-123)
		tmp = Float64(b * Float64(Float64(1.0 / z) / c));
	else
		tmp = Float64(t * Float64(Float64(a * -4.0) / c));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -1.3e+49)
		tmp = a * ((t * -4.0) / c);
	elseif (t <= 1.6e-123)
		tmp = b * ((1.0 / z) / c);
	else
		tmp = t * ((a * -4.0) / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -1.3e+49], N[(a * N[(N[(t * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e-123], N[(b * N[(N[(1.0 / z), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(a * -4.0), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.29999999999999994e49

   1. Initial program 68.6%

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

   3. Simplified 74.5%

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

   5. Taylor expanded in t around inf 57.1%

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

      1. *-commutative 57.1%

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

      2. associate-/l* 66.6%

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

      3. associate-*r* 66.6%

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

      4. *-commutative 66.6%

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

      5. *-commutative 66.6%

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

      6. associate-*l/ 66.6%

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

   7. Simplified 66.6%

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

   if -1.29999999999999994e49 < t < 1.59999999999999989e-123

   1. Initial program 86.0%

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

   3. Simplified 83.2%

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

   5. Taylor expanded in b around inf 48.5%

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

      1. *-commutative 48.5%

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

   7. Simplified 48.5%

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

      1. div-inv 48.5%

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

   9. Applied egg-rr 48.5%

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

   10. Taylor expanded in z around 0 48.5%

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

       1. *-commutative 48.5%

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

       2. associate-/r* 50.1%

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

   12. Simplified 50.1%

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

   if 1.59999999999999989e-123 < t

   1. Initial program 79.0%

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

   3. Simplified 79.1%

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

   5. Taylor expanded in z around 0 75.2%

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

   6. Taylor expanded in a around inf 48.0%

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

      1. associate-*r/ 48.0%

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

      2. associate-*r* 48.1%

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

      3. associate-*l/ 56.7%

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

      4. *-commutative 56.7%

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

   8. Simplified 56.7%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-123}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 33.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b, c] = \mathsf{sort}([x, y, z, t, a, b, c])\\ \\ \begin{array}{l} \mathbf{if}\;c \leq 1.2 \cdot 10^{+223}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c 1.2e+223) (/ (/ b z) c) (/ (/ b c) z)))

C

assert(x < y && y < z && z < t && t < a && a < b && b < c);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 1.2e+223) {
		tmp = (b / z) / c;
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, b, and c 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 (c <= 1.2d+223) then
        tmp = (b / z) / c
    else
        tmp = (b / c) / z
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b && b < c;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 1.2e+223) {
		tmp = (b / z) / c;
	} else {
		tmp = (b / c) / z;
	}
	return tmp;
}

Python

[x, y, z, t, a, b, c] = sort([x, y, z, t, a, b, c])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= 1.2e+223:
		tmp = (b / z) / c
	else:
		tmp = (b / c) / z
	return tmp

Julia

x, y, z, t, a, b, c = sort([x, y, z, t, a, b, c])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= 1.2e+223)
		tmp = Float64(Float64(b / z) / c);
	else
		tmp = Float64(Float64(b / c) / z);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b, c = num2cell(sort([x, y, z, t, a, b, c])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= 1.2e+223)
		tmp = (b / z) / c;
	else
		tmp = (b / c) / z;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, 1.2e+223], N[(N[(b / z), $MachinePrecision] / c), $MachinePrecision], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < 1.20000000000000006e223

   1. Initial program 82.1%

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

   3. Simplified 82.1%

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

   6. Applied egg-rr 53.7%

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

   7. Taylor expanded in b around inf 33.7%

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

      1. associate-*r/ 36.1%

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

   9. Applied egg-rr 36.1%

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

   10. Taylor expanded in z around 0 36.1%

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

   if 1.20000000000000006e223 < c

   1. Initial program 57.0%

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

   3. Simplified 56.6%

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

   6. Applied egg-rr 56.3%

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

   7. Taylor expanded in b around inf 35.3%

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

      1. associate-*l/ 35.4%

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

      2. *-un-lft-identity 35.4%

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

   9. Applied egg-rr 35.4%

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

Alternative 13: 35.2% accurate, 3.8× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, b, and c should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c) :precision binary64 (/ b (* z c)))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x, y, z, t, a, b, and c 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 79.9%

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

3. Simplified 79.9%

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

5. Taylor expanded in b around inf 35.3%

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

   1. *-commutative 35.3%

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

7. Simplified 35.3%

   \[\leadsto \color{blue}{\frac{b}{z \cdot c}} \]
8. Add Preprocessing

Developer Target 1: 80.6% accurate, 0.1× 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 2024136 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) -220031348160821/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 0) (/ (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 365902434742109/31250000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 28768236795461370000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (+ (* (* 9 (/ y c)) (/ x z)) (/ b (* c z))) (* 4 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 138385150424563190000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (- (+ (* 9 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4 (/ (* a t) c)))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))