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

Percentage Accurate: 79.3% → 87.1%

Time: 24.2s

Alternatives: 18

Speedup: 0.8×

• 36.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 79.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 87.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := x \cdot \left(9 \cdot y\right)\\ t_2 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_3 := \frac{\frac{b + \left(t_1 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z}}{c}\\ \mathbf{if}\;t_2 \leq 10^{-43}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 10^{+290}:\\ \;\;\;\;\frac{b + \left(t_1 - a \cdot \left(z \cdot \left(4 \cdot t\right)\right)\right)}{z \cdot c}\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* x (* 9.0 y)))
        (t_2 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))
        (t_3 (/ (/ (+ b (- t_1 (* (* z 4.0) (* t a)))) z) c)))
   (if (<= t_2 1e-43)
     t_3
     (if (<= t_2 1e+290)
       (/ (+ b (- t_1 (* a (* z (* 4.0 t))))) (* z c))
       (if (<= t_2 INFINITY) t_3 (* (/ (* t a) c) -4.0))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x * (9.0 * y);
	double t_2 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double t_3 = ((b + (t_1 - ((z * 4.0) * (t * a)))) / z) / c;
	double tmp;
	if (t_2 <= 1e-43) {
		tmp = t_3;
	} else if (t_2 <= 1e+290) {
		tmp = (b + (t_1 - (a * (z * (4.0 * t))))) / (z * c);
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = ((t * a) / c) * -4.0;
	}
	return tmp;
}

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x * (9.0 * y);
	double t_2 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double t_3 = ((b + (t_1 - ((z * 4.0) * (t * a)))) / z) / c;
	double tmp;
	if (t_2 <= 1e-43) {
		tmp = t_3;
	} else if (t_2 <= 1e+290) {
		tmp = (b + (t_1 - (a * (z * (4.0 * t))))) / (z * c);
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = ((t * a) / c) * -4.0;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = x * (9.0 * y)
	t_2 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)
	t_3 = ((b + (t_1 - ((z * 4.0) * (t * a)))) / z) / c
	tmp = 0
	if t_2 <= 1e-43:
		tmp = t_3
	elif t_2 <= 1e+290:
		tmp = (b + (t_1 - (a * (z * (4.0 * t))))) / (z * c)
	elif t_2 <= math.inf:
		tmp = t_3
	else:
		tmp = ((t * a) / c) * -4.0
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(x * Float64(9.0 * y))
	t_2 = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	t_3 = Float64(Float64(Float64(b + Float64(t_1 - Float64(Float64(z * 4.0) * Float64(t * a)))) / z) / c)
	tmp = 0.0
	if (t_2 <= 1e-43)
		tmp = t_3;
	elseif (t_2 <= 1e+290)
		tmp = Float64(Float64(b + Float64(t_1 - Float64(a * Float64(z * Float64(4.0 * t))))) / Float64(z * c));
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(Float64(Float64(t * a) / c) * -4.0);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x * (9.0 * y);
	t_2 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	t_3 = ((b + (t_1 - ((z * 4.0) * (t * a)))) / z) / c;
	tmp = 0.0;
	if (t_2 <= 1e-43)
		tmp = t_3;
	elseif (t_2 <= 1e+290)
		tmp = (b + (t_1 - (a * (z * (4.0 * t))))) / (z * c);
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = ((t * a) / c) * -4.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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]}, Block[{t$95$3 = N[(N[(N[(b + N[(t$95$1 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[t$95$2, 1e-43], t$95$3, If[LessEqual[t$95$2, 1e+290], N[(N[(b + N[(t$95$1 - N[(a * N[(z * N[(4.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$3, N[(N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 1.00000000000000008e-43 or 1.00000000000000006e290 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 83.0%

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

      1. associate-+l- 83.0%

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

      2. *-commutative 83.0%

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

      3. associate-*r* 80.9%

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

      4. *-commutative 80.9%

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

      5. associate-+l- 80.9%

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

   3. Simplified 84.0%

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

      1. *-un-lft-identity 84.0%

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

      2. times-frac 87.7%

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

      3. associate-+l- 87.7%

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

      4. associate-*r* 87.2%

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

      5. associate-+l- 87.2%

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

      6. associate-*l* 87.2%

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

      7. associate-*r* 87.8%

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

   5. Applied egg-rr 87.8%

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

      1. associate-*l/ 87.9%

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

      2. *-un-lft-identity 87.9%

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

      3. div-inv 87.8%

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

      4. associate-*l/ 90.1%

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

      5. un-div-inv 90.2%

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

   7. Applied egg-rr 90.2%

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

   if 1.00000000000000008e-43 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 1.00000000000000006e290

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-*r* 97.0%

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

      4. *-commutative 97.0%

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

      5. associate-+l- 97.0%

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

   3. Simplified 94.6%

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

      1. associate-*r* 99.6%

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

      2. cancel-sign-sub-inv 99.6%

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

      3. associate-*l* 99.6%

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

      4. associate-*l* 99.6%

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

   5. Applied egg-rr 99.6%

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

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

   1. Initial program 0.0%

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

      1. associate-+l- 0.0%

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

      2. *-commutative 0.0%

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

      3. associate-*r* 1.0%

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

      4. *-commutative 1.0%

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

      5. associate-+l- 1.0%

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

   3. Simplified 1.0%

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

   4. Taylor expanded in z around inf 59.6%

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

      1. *-commutative 59.6%

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

   6. Simplified 59.6%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 10^{-43}:\\ \;\;\;\;\frac{\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z}}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 10^{+290}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - a \cdot \left(z \cdot \left(4 \cdot t\right)\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \end{array} \]

Alternative 2: 86.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{\left(t_1 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{-209}:\\ \;\;\;\;\frac{b + \left(t_1 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{\frac{1}{z} \cdot \left(b + 9 \cdot \left(x \cdot y\right)\right)}{c}\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y))
        (t_2 (/ (+ (- t_1 (* (* (* z 4.0) t) a)) b) (* z c))))
   (if (<= t_2 -5e-209)
     (/ (+ b (- t_1 (* (* z 4.0) (* t a)))) (* z c))
     (if (<= t_2 0.0)
       (/ (* (/ 1.0 z) (+ b (* 9.0 (* x y)))) c)
       (if (<= t_2 INFINITY) t_2 (* (/ (* t a) c) -4.0))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = ((t_1 - (((z * 4.0) * t) * a)) + b) / (z * c);
	double tmp;
	if (t_2 <= -5e-209) {
		tmp = (b + (t_1 - ((z * 4.0) * (t * a)))) / (z * c);
	} else if (t_2 <= 0.0) {
		tmp = ((1.0 / z) * (b + (9.0 * (x * y)))) / c;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = ((t * a) / c) * -4.0;
	}
	return tmp;
}

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = ((t_1 - (((z * 4.0) * t) * a)) + b) / (z * c);
	double tmp;
	if (t_2 <= -5e-209) {
		tmp = (b + (t_1 - ((z * 4.0) * (t * a)))) / (z * c);
	} else if (t_2 <= 0.0) {
		tmp = ((1.0 / z) * (b + (9.0 * (x * y)))) / c;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = ((t * a) / c) * -4.0;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (x * 9.0) * y
	t_2 = ((t_1 - (((z * 4.0) * t) * a)) + b) / (z * c)
	tmp = 0
	if t_2 <= -5e-209:
		tmp = (b + (t_1 - ((z * 4.0) * (t * a)))) / (z * c)
	elif t_2 <= 0.0:
		tmp = ((1.0 / z) * (b + (9.0 * (x * y)))) / c
	elif t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = ((t * a) / c) * -4.0
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	t_2 = Float64(Float64(Float64(t_1 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	tmp = 0.0
	if (t_2 <= -5e-209)
		tmp = Float64(Float64(b + Float64(t_1 - Float64(Float64(z * 4.0) * Float64(t * a)))) / Float64(z * c));
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(Float64(1.0 / z) * Float64(b + Float64(9.0 * Float64(x * y)))) / c);
	elseif (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(t * a) / c) * -4.0);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * 9.0) * y;
	t_2 = ((t_1 - (((z * 4.0) * t) * a)) + b) / (z * c);
	tmp = 0.0;
	if (t_2 <= -5e-209)
		tmp = (b + (t_1 - ((z * 4.0) * (t * a)))) / (z * c);
	elseif (t_2 <= 0.0)
		tmp = ((1.0 / z) * (b + (9.0 * (x * y)))) / c;
	elseif (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = ((t * a) / c) * -4.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$1 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-209], N[(N[(b + N[(t$95$1 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(N[(N[(1.0 / z), $MachinePrecision] * N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$2, N[(N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -5.0000000000000005e-209

   1. Initial program 89.6%

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

      1. associate-+l- 89.6%

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

      2. *-commutative 89.6%

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

      3. associate-*r* 86.0%

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

      4. *-commutative 86.0%

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

      5. associate-+l- 86.0%

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

   3. Simplified 90.6%

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

   if -5.0000000000000005e-209 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -0.0

   1. Initial program 34.9%

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

      1. associate-+l- 34.9%

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

      2. *-commutative 34.9%

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

      3. associate-*r* 28.4%

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

      4. *-commutative 28.4%

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

      5. associate-+l- 28.4%

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

   3. Simplified 34.9%

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

      1. *-un-lft-identity 34.9%

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

      2. times-frac 99.5%

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

      3. associate-+l- 99.5%

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

      4. associate-*r* 99.4%

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

      5. associate-+l- 99.4%

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

      6. associate-*l* 99.3%

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

      7. associate-*r* 99.5%

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

   5. Applied egg-rr 99.5%

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

      1. associate-*r/ 99.5%

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

   7. Applied egg-rr 99.5%

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

   8. Taylor expanded in x around inf 69.7%

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

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

   1. Initial program 90.6%

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

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

   1. Initial program 0.0%

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

      1. associate-+l- 0.0%

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

      2. *-commutative 0.0%

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

      3. associate-*r* 1.0%

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

      4. *-commutative 1.0%

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

      5. associate-+l- 1.0%

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

   3. Simplified 1.0%

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

   4. Taylor expanded in z around inf 59.6%

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

      1. *-commutative 59.6%

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

   6. Simplified 59.6%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -5 \cdot 10^{-209}:\\ \;\;\;\;\frac{b + \left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{\frac{1}{z} \cdot \left(b + 9 \cdot \left(x \cdot y\right)\right)}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \end{array} \]

Alternative 3: 87.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_2 := \frac{\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z}}{c}\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 10^{+290}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))
        (t_2 (/ (/ (+ b (- (* x (* 9.0 y)) (* (* z 4.0) (* t a)))) z) c)))
   (if (<= t_1 5e+52)
     t_2
     (if (<= t_1 1e+290)
       t_1
       (if (<= t_1 INFINITY) t_2 (* (/ (* t a) c) -4.0))))))

C

assert(t < a);
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 t_2 = ((b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / z) / c;
	double tmp;
	if (t_1 <= 5e+52) {
		tmp = t_2;
	} else if (t_1 <= 1e+290) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = ((t * a) / c) * -4.0;
	}
	return tmp;
}

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double t_2 = ((b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / z) / c;
	double tmp;
	if (t_1 <= 5e+52) {
		tmp = t_2;
	} else if (t_1 <= 1e+290) {
		tmp = t_1;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = ((t * a) / c) * -4.0;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)
	t_2 = ((b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / z) / c
	tmp = 0
	if t_1 <= 5e+52:
		tmp = t_2
	elif t_1 <= 1e+290:
		tmp = t_1
	elif t_1 <= math.inf:
		tmp = t_2
	else:
		tmp = ((t * a) / c) * -4.0
	return tmp

Julia

t, a = sort([t, a])
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))
	t_2 = Float64(Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(t * a)))) / z) / c)
	tmp = 0.0
	if (t_1 <= 5e+52)
		tmp = t_2;
	elseif (t_1 <= 1e+290)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(t * a) / c) * -4.0);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
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);
	t_2 = ((b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / z) / c;
	tmp = 0.0;
	if (t_1 <= 5e+52)
		tmp = t_2;
	elseif (t_1 <= 1e+290)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = ((t * a) / c) * -4.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(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]}, Block[{t$95$2 = N[(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] / z), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+52], t$95$2, If[LessEqual[t$95$1, 1e+290], t$95$1, If[LessEqual[t$95$1, Infinity], t$95$2, N[(N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 5e52 or 1.00000000000000006e290 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 83.5%

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

      1. associate-+l- 83.5%

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

      2. *-commutative 83.5%

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

      3. associate-*r* 81.5%

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

      4. *-commutative 81.5%

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

      5. associate-+l- 81.5%

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

   3. Simplified 84.5%

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

      1. *-un-lft-identity 84.5%

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

      2. times-frac 87.7%

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

      3. associate-+l- 87.7%

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

      4. associate-*r* 87.1%

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

      5. associate-+l- 87.1%

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

      6. associate-*l* 87.2%

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

      7. associate-*r* 87.7%

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

   5. Applied egg-rr 87.7%

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

      1. associate-*l/ 87.8%

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

      2. *-un-lft-identity 87.8%

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

      3. div-inv 87.7%

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

      4. associate-*l/ 90.4%

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

      5. un-div-inv 90.5%

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

   7. Applied egg-rr 90.5%

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

   if 5e52 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 1.00000000000000006e290

   1. Initial program 99.6%

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

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

   1. Initial program 0.0%

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

      1. associate-+l- 0.0%

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

      2. *-commutative 0.0%

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

      3. associate-*r* 1.0%

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

      4. *-commutative 1.0%

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

      5. associate-+l- 1.0%

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

   3. Simplified 1.0%

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

   4. Taylor expanded in z around inf 59.6%

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

      1. *-commutative 59.6%

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

   6. Simplified 59.6%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 5 \cdot 10^{+52}:\\ \;\;\;\;\frac{\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z}}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 10^{+290}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \end{array} \]

Alternative 4: 85.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{\left(t_1 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_3 := \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{-246}:\\ \;\;\;\;\frac{b + \left(t_1 - t_3\right)}{z \cdot c}\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \left(x \cdot \left(9 \cdot y\right) - t_3\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (* x 9.0) y))
        (t_2 (/ (+ (- t_1 (* (* (* z 4.0) t) a)) b) (* z c)))
        (t_3 (* (* z 4.0) (* t a))))
   (if (<= t_2 -5e-246)
     (/ (+ b (- t_1 t_3)) (* z c))
     (if (<= t_2 INFINITY)
       (* (/ 1.0 z) (/ (+ b (- (* x (* 9.0 y)) t_3)) c))
       (* (/ (* t a) c) -4.0)))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = ((t_1 - (((z * 4.0) * t) * a)) + b) / (z * c);
	double t_3 = (z * 4.0) * (t * a);
	double tmp;
	if (t_2 <= -5e-246) {
		tmp = (b + (t_1 - t_3)) / (z * c);
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = (1.0 / z) * ((b + ((x * (9.0 * y)) - t_3)) / c);
	} else {
		tmp = ((t * a) / c) * -4.0;
	}
	return tmp;
}

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (x * 9.0) * y;
	double t_2 = ((t_1 - (((z * 4.0) * t) * a)) + b) / (z * c);
	double t_3 = (z * 4.0) * (t * a);
	double tmp;
	if (t_2 <= -5e-246) {
		tmp = (b + (t_1 - t_3)) / (z * c);
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = (1.0 / z) * ((b + ((x * (9.0 * y)) - t_3)) / c);
	} else {
		tmp = ((t * a) / c) * -4.0;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (x * 9.0) * y
	t_2 = ((t_1 - (((z * 4.0) * t) * a)) + b) / (z * c)
	t_3 = (z * 4.0) * (t * a)
	tmp = 0
	if t_2 <= -5e-246:
		tmp = (b + (t_1 - t_3)) / (z * c)
	elif t_2 <= math.inf:
		tmp = (1.0 / z) * ((b + ((x * (9.0 * y)) - t_3)) / c)
	else:
		tmp = ((t * a) / c) * -4.0
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(x * 9.0) * y)
	t_2 = Float64(Float64(Float64(t_1 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	t_3 = Float64(Float64(z * 4.0) * Float64(t * a))
	tmp = 0.0
	if (t_2 <= -5e-246)
		tmp = Float64(Float64(b + Float64(t_1 - t_3)) / Float64(z * c));
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(1.0 / z) * Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - t_3)) / c));
	else
		tmp = Float64(Float64(Float64(t * a) / c) * -4.0);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (x * 9.0) * y;
	t_2 = ((t_1 - (((z * 4.0) * t) * a)) + b) / (z * c);
	t_3 = (z * 4.0) * (t * a);
	tmp = 0.0;
	if (t_2 <= -5e-246)
		tmp = (b + (t_1 - t_3)) / (z * c);
	elseif (t_2 <= Inf)
		tmp = (1.0 / z) * ((b + ((x * (9.0 * y)) - t_3)) / c);
	else
		tmp = ((t * a) / c) * -4.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$1 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-246], N[(N[(b + N[(t$95$1 - t$95$3), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[(N[(1.0 / z), $MachinePrecision] * N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -4.9999999999999997e-246

   1. Initial program 89.8%

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

      1. associate-+l- 89.8%

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

      2. *-commutative 89.8%

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

      3. associate-*r* 86.2%

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

      4. *-commutative 86.2%

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

      5. associate-+l- 86.2%

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

   3. Simplified 90.8%

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

   if -4.9999999999999997e-246 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 82.4%

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

      1. associate-+l- 82.4%

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

      2. *-commutative 82.4%

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

      3. associate-*r* 81.4%

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

      4. *-commutative 81.4%

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

      5. associate-+l- 81.4%

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

   3. Simplified 81.7%

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

      1. *-un-lft-identity 81.7%

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

      2. times-frac 92.3%

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

      3. associate-+l- 92.3%

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

      4. associate-*r* 93.0%

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

      5. associate-+l- 93.0%

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

      6. associate-*l* 93.0%

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

      7. associate-*r* 92.3%

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

   5. Applied egg-rr 92.3%

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

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

   1. Initial program 0.0%

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

      1. associate-+l- 0.0%

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

      2. *-commutative 0.0%

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

      3. associate-*r* 1.0%

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

      4. *-commutative 1.0%

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

      5. associate-+l- 1.0%

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

   3. Simplified 1.0%

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

   4. Taylor expanded in z around inf 59.6%

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

      1. *-commutative 59.6%

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

   6. Simplified 59.6%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -5 \cdot 10^{-246}:\\ \;\;\;\;\frac{b + \left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \end{array} \]

Alternative 5: 73.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot a}{c} \cdot -4 + \frac{b}{z \cdot c}\\ t_2 := 9 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-106}:\\ \;\;\;\;\frac{b + t_2}{z \cdot c}\\ \mathbf{elif}\;z \leq 5900000:\\ \;\;\;\;\frac{b + \left(t \cdot a\right) \cdot \left(z \cdot -4\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+60}:\\ \;\;\;\;\frac{t_2 - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* (/ (* t a) c) -4.0) (/ b (* z c)))) (t_2 (* 9.0 (* x y))))
   (if (<= z -6.2e-19)
     t_1
     (if (<= z 4.3e-106)
       (/ (+ b t_2) (* z c))
       (if (<= z 5900000.0)
         (/ (+ b (* (* t a) (* z -4.0))) (* z c))
         (if (<= z 1.02e+60)
           (/ (- t_2 (* 4.0 (* a (* z t)))) (* z c))
           t_1))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (((t * a) / c) * -4.0) + (b / (z * c));
	double t_2 = 9.0 * (x * y);
	double tmp;
	if (z <= -6.2e-19) {
		tmp = t_1;
	} else if (z <= 4.3e-106) {
		tmp = (b + t_2) / (z * c);
	} else if (z <= 5900000.0) {
		tmp = (b + ((t * a) * (z * -4.0))) / (z * c);
	} else if (z <= 1.02e+60) {
		tmp = (t_2 - (4.0 * (a * (z * t)))) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (((t * a) / c) * (-4.0d0)) + (b / (z * c))
    t_2 = 9.0d0 * (x * y)
    if (z <= (-6.2d-19)) then
        tmp = t_1
    else if (z <= 4.3d-106) then
        tmp = (b + t_2) / (z * c)
    else if (z <= 5900000.0d0) then
        tmp = (b + ((t * a) * (z * (-4.0d0)))) / (z * c)
    else if (z <= 1.02d+60) then
        tmp = (t_2 - (4.0d0 * (a * (z * t)))) / (z * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (((t * a) / c) * -4.0) + (b / (z * c));
	double t_2 = 9.0 * (x * y);
	double tmp;
	if (z <= -6.2e-19) {
		tmp = t_1;
	} else if (z <= 4.3e-106) {
		tmp = (b + t_2) / (z * c);
	} else if (z <= 5900000.0) {
		tmp = (b + ((t * a) * (z * -4.0))) / (z * c);
	} else if (z <= 1.02e+60) {
		tmp = (t_2 - (4.0 * (a * (z * t)))) / (z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (((t * a) / c) * -4.0) + (b / (z * c))
	t_2 = 9.0 * (x * y)
	tmp = 0
	if z <= -6.2e-19:
		tmp = t_1
	elif z <= 4.3e-106:
		tmp = (b + t_2) / (z * c)
	elif z <= 5900000.0:
		tmp = (b + ((t * a) * (z * -4.0))) / (z * c)
	elif z <= 1.02e+60:
		tmp = (t_2 - (4.0 * (a * (z * t)))) / (z * c)
	else:
		tmp = t_1
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(t * a) / c) * -4.0) + Float64(b / Float64(z * c)))
	t_2 = Float64(9.0 * Float64(x * y))
	tmp = 0.0
	if (z <= -6.2e-19)
		tmp = t_1;
	elseif (z <= 4.3e-106)
		tmp = Float64(Float64(b + t_2) / Float64(z * c));
	elseif (z <= 5900000.0)
		tmp = Float64(Float64(b + Float64(Float64(t * a) * Float64(z * -4.0))) / Float64(z * c));
	elseif (z <= 1.02e+60)
		tmp = Float64(Float64(t_2 - Float64(4.0 * Float64(a * Float64(z * t)))) / Float64(z * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (((t * a) / c) * -4.0) + (b / (z * c));
	t_2 = 9.0 * (x * y);
	tmp = 0.0;
	if (z <= -6.2e-19)
		tmp = t_1;
	elseif (z <= 4.3e-106)
		tmp = (b + t_2) / (z * c);
	elseif (z <= 5900000.0)
		tmp = (b + ((t * a) * (z * -4.0))) / (z * c);
	elseif (z <= 1.02e+60)
		tmp = (t_2 - (4.0 * (a * (z * t)))) / (z * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.2e-19], t$95$1, If[LessEqual[z, 4.3e-106], N[(N[(b + t$95$2), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5900000.0], N[(N[(b + N[(N[(t * a), $MachinePrecision] * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e+60], N[(N[(t$95$2 - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.1999999999999998e-19 or 1.0200000000000001e60 < z

   1. Initial program 62.2%

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

      1. associate-+l- 62.2%

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

      2. *-commutative 62.2%

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

      3. associate-*r* 59.1%

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

      4. *-commutative 59.1%

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

      5. associate-+l- 59.1%

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

   3. Simplified 65.5%

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

   4. Taylor expanded in x around 0 52.7%

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

      1. associate-*r* 55.3%

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

      2. *-commutative 55.3%

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

      3. associate-*l* 55.3%

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

      4. *-commutative 55.3%

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

      5. associate-*l* 55.3%

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

      6. *-rgt-identity 55.3%

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

      7. cancel-sign-sub-inv 55.3%

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

      8. *-rgt-identity 55.3%

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

      9. *-commutative 55.3%

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

      10. distribute-rgt-neg-in 55.3%

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

      11. *-commutative 55.3%

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

      12. distribute-rgt-neg-in 55.3%

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

      13. metadata-eval 55.3%

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

      14. *-commutative 55.3%

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

   6. Simplified 55.3%

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

   7. Taylor expanded in b around 0 72.5%

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

   if -6.1999999999999998e-19 < z < 4.3000000000000002e-106

   1. Initial program 95.3%

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

      1. associate-+l- 95.3%

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

      2. *-commutative 95.3%

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

      3. associate-*r* 94.4%

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

      4. *-commutative 94.4%

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

      5. associate-+l- 94.4%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in x around inf 85.9%

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

   if 4.3000000000000002e-106 < z < 5.9e6

   1. Initial program 94.1%

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

      1. associate-+l- 94.1%

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

      2. *-commutative 94.1%

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

      3. associate-*r* 93.9%

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

      4. *-commutative 93.9%

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

      5. associate-+l- 93.9%

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

   3. Simplified 88.4%

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

   4. Taylor expanded in x around 0 82.9%

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

      1. associate-*r* 77.2%

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

      2. *-commutative 77.2%

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

      3. associate-*l* 77.2%

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

      4. *-commutative 77.2%

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

      5. associate-*l* 77.2%

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

      6. *-rgt-identity 77.2%

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

      7. cancel-sign-sub-inv 77.2%

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

      8. *-rgt-identity 77.2%

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

      9. *-commutative 77.2%

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

      10. distribute-rgt-neg-in 77.2%

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

      11. *-commutative 77.2%

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

      12. distribute-rgt-neg-in 77.2%

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

      13. metadata-eval 77.2%

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

      14. *-commutative 77.2%

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

   6. Simplified 77.2%

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

   if 5.9e6 < z < 1.0200000000000001e60

   1. Initial program 99.2%

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

      1. associate-+l- 99.2%

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

      2. *-commutative 99.2%

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

      3. associate-*r* 99.1%

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

      4. *-commutative 99.1%

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

      5. associate-+l- 99.1%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in b around 0 79.0%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-19}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4 + \frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-106}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 5900000:\\ \;\;\;\;\frac{b + \left(t \cdot a\right) \cdot \left(z \cdot -4\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+60}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4 + \frac{b}{z \cdot c}\\ \end{array} \]

Alternative 6: 73.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot a}{c} \cdot -4 + \frac{b}{z \cdot c}\\ t_2 := 9 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-19}:\\ \;\;\;\;\frac{b + t_2}{z \cdot c}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+107}:\\ \;\;\;\;\frac{\frac{t_2 - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (* (/ (* t a) c) -4.0) (/ b (* z c)))) (t_2 (* 9.0 (* x y))))
   (if (<= z -6.2e-19)
     t_1
     (if (<= z 7.4e-19)
       (/ (+ b t_2) (* z c))
       (if (<= z 2e+107) (/ (/ (- t_2 (* 4.0 (* a (* z t)))) z) c) t_1)))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (((t * a) / c) * -4.0) + (b / (z * c));
	double t_2 = 9.0 * (x * y);
	double tmp;
	if (z <= -6.2e-19) {
		tmp = t_1;
	} else if (z <= 7.4e-19) {
		tmp = (b + t_2) / (z * c);
	} else if (z <= 2e+107) {
		tmp = ((t_2 - (4.0 * (a * (z * t)))) / z) / c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (((t * a) / c) * (-4.0d0)) + (b / (z * c))
    t_2 = 9.0d0 * (x * y)
    if (z <= (-6.2d-19)) then
        tmp = t_1
    else if (z <= 7.4d-19) then
        tmp = (b + t_2) / (z * c)
    else if (z <= 2d+107) then
        tmp = ((t_2 - (4.0d0 * (a * (z * t)))) / z) / c
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (((t * a) / c) * -4.0) + (b / (z * c));
	double t_2 = 9.0 * (x * y);
	double tmp;
	if (z <= -6.2e-19) {
		tmp = t_1;
	} else if (z <= 7.4e-19) {
		tmp = (b + t_2) / (z * c);
	} else if (z <= 2e+107) {
		tmp = ((t_2 - (4.0 * (a * (z * t)))) / z) / c;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (((t * a) / c) * -4.0) + (b / (z * c))
	t_2 = 9.0 * (x * y)
	tmp = 0
	if z <= -6.2e-19:
		tmp = t_1
	elif z <= 7.4e-19:
		tmp = (b + t_2) / (z * c)
	elif z <= 2e+107:
		tmp = ((t_2 - (4.0 * (a * (z * t)))) / z) / c
	else:
		tmp = t_1
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(t * a) / c) * -4.0) + Float64(b / Float64(z * c)))
	t_2 = Float64(9.0 * Float64(x * y))
	tmp = 0.0
	if (z <= -6.2e-19)
		tmp = t_1;
	elseif (z <= 7.4e-19)
		tmp = Float64(Float64(b + t_2) / Float64(z * c));
	elseif (z <= 2e+107)
		tmp = Float64(Float64(Float64(t_2 - Float64(4.0 * Float64(a * Float64(z * t)))) / z) / c);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (((t * a) / c) * -4.0) + (b / (z * c));
	t_2 = 9.0 * (x * y);
	tmp = 0.0;
	if (z <= -6.2e-19)
		tmp = t_1;
	elseif (z <= 7.4e-19)
		tmp = (b + t_2) / (z * c);
	elseif (z <= 2e+107)
		tmp = ((t_2 - (4.0 * (a * (z * t)))) / z) / c;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.2e-19], t$95$1, If[LessEqual[z, 7.4e-19], N[(N[(b + t$95$2), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+107], N[(N[(N[(t$95$2 - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.1999999999999998e-19 or 1.9999999999999999e107 < z

   1. Initial program 60.9%

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

      1. associate-+l- 60.9%

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

      2. *-commutative 60.9%

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

      3. associate-*r* 57.6%

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

      4. *-commutative 57.6%

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

      5. associate-+l- 57.6%

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

   3. Simplified 64.5%

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

   4. Taylor expanded in x around 0 52.4%

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

      1. associate-*r* 55.2%

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

      2. *-commutative 55.2%

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

      3. associate-*l* 55.2%

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

      4. *-commutative 55.2%

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

      5. associate-*l* 55.2%

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

      6. *-rgt-identity 55.2%

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

      7. cancel-sign-sub-inv 55.2%

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

      8. *-rgt-identity 55.2%

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

      9. *-commutative 55.2%

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

      10. distribute-rgt-neg-in 55.2%

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

      11. *-commutative 55.2%

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

      12. distribute-rgt-neg-in 55.2%

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

      13. metadata-eval 55.2%

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

      14. *-commutative 55.2%

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

   6. Simplified 55.2%

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

   7. Taylor expanded in b around 0 73.7%

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

   if -6.1999999999999998e-19 < z < 7.40000000000000011e-19

   1. Initial program 94.9%

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

      1. associate-+l- 94.9%

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

      2. *-commutative 94.9%

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

      3. associate-*r* 94.1%

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

      4. *-commutative 94.1%

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

      5. associate-+l- 94.1%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in x around inf 82.4%

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

   if 7.40000000000000011e-19 < z < 1.9999999999999999e107

   1. Initial program 91.9%

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

      1. associate-+l- 91.9%

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

      2. *-commutative 91.9%

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

      3. associate-*r* 91.7%

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

      4. *-commutative 91.7%

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

      5. associate-+l- 91.7%

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

   3. Simplified 91.9%

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

      1. *-un-lft-identity 91.9%

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

      2. times-frac 91.9%

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

      3. associate-+l- 91.9%

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

      4. associate-*r* 92.0%

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

      5. associate-+l- 92.0%

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

      6. associate-*l* 92.2%

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

      7. associate-*r* 92.1%

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

   5. Applied egg-rr 92.1%

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

      1. associate-*l/ 92.0%

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

      2. *-un-lft-identity 92.0%

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

      3. div-inv 91.8%

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

      4. associate-*l/ 95.6%

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

      5. un-div-inv 95.9%

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

   7. Applied egg-rr 95.9%

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

   8. Taylor expanded in b around 0 82.9%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-19}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4 + \frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-19}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+107}:\\ \;\;\;\;\frac{\frac{9 \cdot \left(x \cdot y\right) - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4 + \frac{b}{z \cdot c}\\ \end{array} \]

Alternative 7: 84.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+163} \lor \neg \left(z \leq 1.02 \cdot 10^{+152}\right):\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4 + \frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.22e+163) (not (<= z 1.02e+152)))
   (+ (* (/ (* t a) c) -4.0) (/ b (* z c)))
   (/ (+ b (- (* (* x 9.0) y) (* (* z 4.0) (* t a)))) (* z c))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.22e+163) || !(z <= 1.02e+152)) {
		tmp = (((t * a) / c) * -4.0) + (b / (z * c));
	} else {
		tmp = (b + (((x * 9.0) * y) - ((z * 4.0) * (t * a)))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-1.22d+163)) .or. (.not. (z <= 1.02d+152))) then
        tmp = (((t * a) / c) * (-4.0d0)) + (b / (z * c))
    else
        tmp = (b + (((x * 9.0d0) * y) - ((z * 4.0d0) * (t * a)))) / (z * c)
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.22e+163) || !(z <= 1.02e+152)) {
		tmp = (((t * a) / c) * -4.0) + (b / (z * c));
	} else {
		tmp = (b + (((x * 9.0) * y) - ((z * 4.0) * (t * a)))) / (z * c);
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -1.22e+163) or not (z <= 1.02e+152):
		tmp = (((t * a) / c) * -4.0) + (b / (z * c))
	else:
		tmp = (b + (((x * 9.0) * y) - ((z * 4.0) * (t * a)))) / (z * c)
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.22e+163) || !(z <= 1.02e+152))
		tmp = Float64(Float64(Float64(Float64(t * a) / c) * -4.0) + Float64(b / Float64(z * c)));
	else
		tmp = Float64(Float64(b + Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(z * 4.0) * Float64(t * a)))) / Float64(z * c));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -1.22e+163) || ~((z <= 1.02e+152)))
		tmp = (((t * a) / c) * -4.0) + (b / (z * c));
	else
		tmp = (b + (((x * 9.0) * y) - ((z * 4.0) * (t * a)))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.22e+163], N[Not[LessEqual[z, 1.02e+152]], $MachinePrecision]], N[(N[(N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.22e163 or 1.01999999999999999e152 < z

   1. Initial program 50.5%

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

      1. associate-+l- 50.5%

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

      2. *-commutative 50.5%

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

      3. associate-*r* 45.2%

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

      4. *-commutative 45.2%

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

      5. associate-+l- 45.2%

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

   3. Simplified 54.9%

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

   4. Taylor expanded in x around 0 46.6%

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

      1. associate-*r* 49.7%

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

      2. *-commutative 49.7%

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

      3. associate-*l* 49.7%

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

      4. *-commutative 49.7%

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

      5. associate-*l* 49.7%

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

      6. *-rgt-identity 49.7%

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

      7. cancel-sign-sub-inv 49.7%

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

      8. *-rgt-identity 49.7%

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

      9. *-commutative 49.7%

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

      10. distribute-rgt-neg-in 49.7%

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

      11. *-commutative 49.7%

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

      12. distribute-rgt-neg-in 49.7%

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

      13. metadata-eval 49.7%

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

      14. *-commutative 49.7%

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

   6. Simplified 49.7%

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

   7. Taylor expanded in b around 0 77.1%

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

   if -1.22e163 < z < 1.01999999999999999e152

   1. Initial program 90.4%

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

      1. associate-+l- 90.4%

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

      2. *-commutative 90.4%

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

      3. associate-*r* 89.8%

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

      4. *-commutative 89.8%

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

      5. associate-+l- 89.8%

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

   3. Simplified 88.9%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+163} \lor \neg \left(z \leq 1.02 \cdot 10^{+152}\right):\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4 + \frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 8: 49.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := \frac{t \cdot a}{c} \cdot -4\\ \mathbf{if}\;b \leq -3.3 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-187}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot \frac{9}{c}\right)}{z}\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-226}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-235}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-17}:\\ \;\;\;\;\frac{x \cdot 9}{z \cdot \frac{c}{y}}\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+58}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (/ b c) z)) (t_2 (* (/ (* t a) c) -4.0)))
   (if (<= b -3.3e+15)
     t_1
     (if (<= b -1.2e-187)
       (/ (* x (* y (/ 9.0 c))) z)
       (if (<= b -3e-226)
         t_2
         (if (<= b 6e-235)
           (* a (* t (/ -4.0 c)))
           (if (<= b 3.1e-17)
             (/ (* x 9.0) (* z (/ c y)))
             (if (<= b 1.4e+58) t_2 t_1))))))))

C

assert(t < a);
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 = ((t * a) / c) * -4.0;
	double tmp;
	if (b <= -3.3e+15) {
		tmp = t_1;
	} else if (b <= -1.2e-187) {
		tmp = (x * (y * (9.0 / c))) / z;
	} else if (b <= -3e-226) {
		tmp = t_2;
	} else if (b <= 6e-235) {
		tmp = a * (t * (-4.0 / c));
	} else if (b <= 3.1e-17) {
		tmp = (x * 9.0) / (z * (c / y));
	} else if (b <= 1.4e+58) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b / c) / z
    t_2 = ((t * a) / c) * (-4.0d0)
    if (b <= (-3.3d+15)) then
        tmp = t_1
    else if (b <= (-1.2d-187)) then
        tmp = (x * (y * (9.0d0 / c))) / z
    else if (b <= (-3d-226)) then
        tmp = t_2
    else if (b <= 6d-235) then
        tmp = a * (t * ((-4.0d0) / c))
    else if (b <= 3.1d-17) then
        tmp = (x * 9.0d0) / (z * (c / y))
    else if (b <= 1.4d+58) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double t_2 = ((t * a) / c) * -4.0;
	double tmp;
	if (b <= -3.3e+15) {
		tmp = t_1;
	} else if (b <= -1.2e-187) {
		tmp = (x * (y * (9.0 / c))) / z;
	} else if (b <= -3e-226) {
		tmp = t_2;
	} else if (b <= 6e-235) {
		tmp = a * (t * (-4.0 / c));
	} else if (b <= 3.1e-17) {
		tmp = (x * 9.0) / (z * (c / y));
	} else if (b <= 1.4e+58) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (b / c) / z
	t_2 = ((t * a) / c) * -4.0
	tmp = 0
	if b <= -3.3e+15:
		tmp = t_1
	elif b <= -1.2e-187:
		tmp = (x * (y * (9.0 / c))) / z
	elif b <= -3e-226:
		tmp = t_2
	elif b <= 6e-235:
		tmp = a * (t * (-4.0 / c))
	elif b <= 3.1e-17:
		tmp = (x * 9.0) / (z * (c / y))
	elif b <= 1.4e+58:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b / c) / z)
	t_2 = Float64(Float64(Float64(t * a) / c) * -4.0)
	tmp = 0.0
	if (b <= -3.3e+15)
		tmp = t_1;
	elseif (b <= -1.2e-187)
		tmp = Float64(Float64(x * Float64(y * Float64(9.0 / c))) / z);
	elseif (b <= -3e-226)
		tmp = t_2;
	elseif (b <= 6e-235)
		tmp = Float64(a * Float64(t * Float64(-4.0 / c)));
	elseif (b <= 3.1e-17)
		tmp = Float64(Float64(x * 9.0) / Float64(z * Float64(c / y)));
	elseif (b <= 1.4e+58)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b / c) / z;
	t_2 = ((t * a) / c) * -4.0;
	tmp = 0.0;
	if (b <= -3.3e+15)
		tmp = t_1;
	elseif (b <= -1.2e-187)
		tmp = (x * (y * (9.0 / c))) / z;
	elseif (b <= -3e-226)
		tmp = t_2;
	elseif (b <= 6e-235)
		tmp = a * (t * (-4.0 / c));
	elseif (b <= 3.1e-17)
		tmp = (x * 9.0) / (z * (c / y));
	elseif (b <= 1.4e+58)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision]}, If[LessEqual[b, -3.3e+15], t$95$1, If[LessEqual[b, -1.2e-187], N[(N[(x * N[(y * N[(9.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, -3e-226], t$95$2, If[LessEqual[b, 6e-235], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.1e-17], N[(N[(x * 9.0), $MachinePrecision] / N[(z * N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.4e+58], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.3e15 or 1.3999999999999999e58 < b

   1. Initial program 84.0%

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

      1. associate-+l- 84.0%

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

      2. *-commutative 84.0%

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

      3. associate-*r* 84.1%

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

      4. *-commutative 84.1%

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

      5. associate-+l- 84.1%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in b around inf 50.3%

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

      1. associate-/r* 58.6%

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

   6. Simplified 58.6%

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

   if -3.3e15 < b < -1.20000000000000007e-187

   1. Initial program 85.8%

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

      1. associate-+l- 85.8%

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

      2. *-commutative 85.8%

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

      3. associate-*r* 85.8%

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

      4. *-commutative 85.8%

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

      5. associate-+l- 85.8%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in x around inf 52.2%

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

      1. associate-*r/ 52.2%

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

      2. associate-*r* 52.2%

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

      3. *-commutative 52.2%

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

      4. associate-*r* 52.2%

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

      5. *-commutative 52.2%

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

      6. times-frac 50.3%

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

      7. associate-/l* 50.3%

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

   6. Simplified 50.3%

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

      1. associate-*l/ 56.8%

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

      2. associate-/r/ 56.9%

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

   8. Applied egg-rr 56.9%

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

   if -1.20000000000000007e-187 < b < -2.99999999999999995e-226 or 3.0999999999999998e-17 < b < 1.3999999999999999e58

   1. Initial program 65.8%

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

      1. associate-+l- 65.8%

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

      2. *-commutative 65.8%

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

      3. associate-*r* 65.8%

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

      4. *-commutative 65.8%

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

      5. associate-+l- 65.8%

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

   3. Simplified 66.0%

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

   4. Taylor expanded in z around inf 72.0%

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

      1. *-commutative 72.0%

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

   6. Simplified 72.0%

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

   if -2.99999999999999995e-226 < b < 5.9999999999999997e-235

   1. Initial program 62.2%

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

      1. associate-+l- 62.2%

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

      2. *-commutative 62.2%

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

      3. associate-*r* 56.6%

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

      4. *-commutative 56.6%

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

      5. associate-+l- 56.6%

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

   3. Simplified 62.3%

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

      1. *-un-lft-identity 62.3%

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

      2. times-frac 72.7%

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

      3. associate-+l- 72.7%

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

      4. associate-*r* 72.7%

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

      5. associate-+l- 72.7%

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

      6. associate-*l* 72.7%

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

      7. associate-*r* 72.7%

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

   5. Applied egg-rr 72.7%

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

      1. associate-*r/ 72.8%

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

   7. Applied egg-rr 72.8%

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

   8. Taylor expanded in z around inf 53.5%

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

      1. associate-*r/ 53.5%

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

      2. *-commutative 53.5%

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

      3. associate-*l/ 53.4%

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

      4. *-commutative 53.4%

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

      5. *-commutative 53.4%

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

      6. associate-*l* 50.8%

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

   10. Simplified 50.8%

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

   if 5.9999999999999997e-235 < b < 3.0999999999999998e-17

   1. Initial program 82.3%

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

      1. associate-+l- 82.3%

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

      2. *-commutative 82.3%

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

      3. associate-*r* 74.8%

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

      4. *-commutative 74.8%

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

      5. associate-+l- 74.8%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in x around inf 55.5%

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

      1. associate-*r/ 55.5%

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

      2. associate-*r* 55.5%

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

      3. *-commutative 55.5%

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

      4. associate-*r* 55.5%

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

      5. *-commutative 55.5%

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

      6. times-frac 63.1%

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

      7. associate-/l* 63.0%

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

   6. Simplified 63.0%

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

      1. frac-times 58.4%

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

   8. Applied egg-rr 58.4%

      \[\leadsto \color{blue}{\frac{x \cdot 9}{z \cdot \frac{c}{y}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+15}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-187}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot \frac{9}{c}\right)}{z}\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-226}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-235}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-17}:\\ \;\;\;\;\frac{x \cdot 9}{z \cdot \frac{c}{y}}\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+58}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 9: 49.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;b \leq -6 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-235}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-197}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9}{\frac{c}{y}}\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-17}:\\ \;\;\;\;9 \cdot \frac{\frac{x}{c}}{\frac{z}{y}}\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+59}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (/ b c) z)))
   (if (<= b -6e+15)
     t_1
     (if (<= b 2.2e-235)
       (* a (* t (/ -4.0 c)))
       (if (<= b 4.2e-197)
         (* (/ x z) (/ 9.0 (/ c y)))
         (if (<= b 1.7e-17)
           (* 9.0 (/ (/ x c) (/ z y)))
           (if (<= b 2e+59) (* (/ (* t a) c) -4.0) t_1)))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double tmp;
	if (b <= -6e+15) {
		tmp = t_1;
	} else if (b <= 2.2e-235) {
		tmp = a * (t * (-4.0 / c));
	} else if (b <= 4.2e-197) {
		tmp = (x / z) * (9.0 / (c / y));
	} else if (b <= 1.7e-17) {
		tmp = 9.0 * ((x / c) / (z / y));
	} else if (b <= 2e+59) {
		tmp = ((t * a) / c) * -4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b / c) / z
    if (b <= (-6d+15)) then
        tmp = t_1
    else if (b <= 2.2d-235) then
        tmp = a * (t * ((-4.0d0) / c))
    else if (b <= 4.2d-197) then
        tmp = (x / z) * (9.0d0 / (c / y))
    else if (b <= 1.7d-17) then
        tmp = 9.0d0 * ((x / c) / (z / y))
    else if (b <= 2d+59) then
        tmp = ((t * a) / c) * (-4.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double tmp;
	if (b <= -6e+15) {
		tmp = t_1;
	} else if (b <= 2.2e-235) {
		tmp = a * (t * (-4.0 / c));
	} else if (b <= 4.2e-197) {
		tmp = (x / z) * (9.0 / (c / y));
	} else if (b <= 1.7e-17) {
		tmp = 9.0 * ((x / c) / (z / y));
	} else if (b <= 2e+59) {
		tmp = ((t * a) / c) * -4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (b / c) / z
	tmp = 0
	if b <= -6e+15:
		tmp = t_1
	elif b <= 2.2e-235:
		tmp = a * (t * (-4.0 / c))
	elif b <= 4.2e-197:
		tmp = (x / z) * (9.0 / (c / y))
	elif b <= 1.7e-17:
		tmp = 9.0 * ((x / c) / (z / y))
	elif b <= 2e+59:
		tmp = ((t * a) / c) * -4.0
	else:
		tmp = t_1
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b / c) / z)
	tmp = 0.0
	if (b <= -6e+15)
		tmp = t_1;
	elseif (b <= 2.2e-235)
		tmp = Float64(a * Float64(t * Float64(-4.0 / c)));
	elseif (b <= 4.2e-197)
		tmp = Float64(Float64(x / z) * Float64(9.0 / Float64(c / y)));
	elseif (b <= 1.7e-17)
		tmp = Float64(9.0 * Float64(Float64(x / c) / Float64(z / y)));
	elseif (b <= 2e+59)
		tmp = Float64(Float64(Float64(t * a) / c) * -4.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b / c) / z;
	tmp = 0.0;
	if (b <= -6e+15)
		tmp = t_1;
	elseif (b <= 2.2e-235)
		tmp = a * (t * (-4.0 / c));
	elseif (b <= 4.2e-197)
		tmp = (x / z) * (9.0 / (c / y));
	elseif (b <= 1.7e-17)
		tmp = 9.0 * ((x / c) / (z / y));
	elseif (b <= 2e+59)
		tmp = ((t * a) / c) * -4.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[b, -6e+15], t$95$1, If[LessEqual[b, 2.2e-235], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.2e-197], N[(N[(x / z), $MachinePrecision] * N[(9.0 / N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e-17], N[(9.0 * N[(N[(x / c), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2e+59], N[(N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -6e15 or 1.99999999999999994e59 < b

   1. Initial program 83.8%

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

      1. associate-+l- 83.8%

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

      2. *-commutative 83.8%

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

      3. associate-*r* 84.0%

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

      4. *-commutative 84.0%

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

      5. associate-+l- 84.0%

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

   3. Simplified 86.4%

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

   4. Taylor expanded in b around inf 50.8%

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

      1. associate-/r* 59.1%

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

   6. Simplified 59.1%

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

   if -6e15 < b < 2.19999999999999984e-235

   1. Initial program 72.4%

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

      1. associate-+l- 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-*r* 70.1%

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

      4. *-commutative 70.1%

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

      5. associate-+l- 70.1%

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

   3. Simplified 71.4%

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

      1. *-un-lft-identity 71.4%

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

      2. times-frac 78.1%

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

      3. associate-+l- 78.1%

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

      4. associate-*r* 78.1%

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

      5. associate-+l- 78.1%

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

      6. associate-*l* 78.1%

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

      7. associate-*r* 78.2%

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

   5. Applied egg-rr 78.2%

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

      1. associate-*r/ 78.3%

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

   7. Applied egg-rr 78.3%

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

   8. Taylor expanded in z around inf 51.3%

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

      1. associate-*r/ 51.3%

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

      2. *-commutative 51.3%

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

      3. associate-*l/ 51.2%

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

      4. *-commutative 51.2%

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

      5. *-commutative 51.2%

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

      6. associate-*l* 51.2%

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

   10. Simplified 51.2%

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

   if 2.19999999999999984e-235 < b < 4.2e-197

   1. Initial program 83.5%

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

      1. associate-+l- 83.5%

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

      2. *-commutative 83.5%

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

      3. associate-*r* 83.5%

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

      4. *-commutative 83.5%

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

      5. associate-+l- 83.5%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in x around inf 83.7%

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

      1. associate-*r/ 83.7%

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

      2. associate-*r* 83.5%

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

      3. *-commutative 83.5%

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

      4. associate-*r* 84.0%

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

      5. *-commutative 84.0%

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

      6. times-frac 68.9%

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

      7. associate-/l* 68.6%

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

   6. Simplified 68.6%

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

   if 4.2e-197 < b < 1.6999999999999999e-17

   1. Initial program 82.1%

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

      1. associate-+l- 82.1%

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

      2. *-commutative 82.1%

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

      3. associate-*r* 73.2%

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

      4. *-commutative 73.2%

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

      5. associate-+l- 73.2%

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

   3. Simplified 76.5%

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

      1. *-un-lft-identity 76.5%

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

      2. times-frac 82.2%

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

      3. associate-+l- 82.2%

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

      4. associate-*r* 84.9%

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

      5. associate-+l- 84.9%

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

      6. associate-*l* 85.0%

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

      7. associate-*r* 82.3%

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

   5. Applied egg-rr 82.3%

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

      1. associate-*l/ 82.5%

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

      2. *-un-lft-identity 82.5%

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

      3. div-inv 82.3%

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

      4. associate-*l/ 82.3%

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

      5. un-div-inv 82.4%

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

   7. Applied egg-rr 82.4%

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

   8. Taylor expanded in x around inf 50.4%

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

      1. times-frac 56.6%

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

      2. associate-*r/ 59.3%

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

      3. associate-/l* 56.6%

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

   10. Simplified 56.6%

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

   if 1.6999999999999999e-17 < b < 1.99999999999999994e59

   1. Initial program 76.6%

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

      1. associate-+l- 76.6%

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

      2. *-commutative 76.6%

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

      3. associate-*r* 76.3%

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

      4. *-commutative 76.3%

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

      5. associate-+l- 76.3%

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

   3. Simplified 76.6%

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

   4. Taylor expanded in z around inf 68.1%

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

      1. *-commutative 68.1%

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

   6. Simplified 68.1%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+15}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-235}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-197}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9}{\frac{c}{y}}\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-17}:\\ \;\;\;\;9 \cdot \frac{\frac{x}{c}}{\frac{z}{y}}\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+59}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 10: 72.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-19} \lor \neg \left(z \leq 1.2 \cdot 10^{-105}\right):\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4 + \frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -1.1e-19) (not (<= z 1.2e-105)))
   (+ (* (/ (* t a) c) -4.0) (/ b (* z c)))
   (/ (+ b (* 9.0 (* x y))) (* z c))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.1e-19) || !(z <= 1.2e-105)) {
		tmp = (((t * a) / c) * -4.0) + (b / (z * c));
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-1.1d-19)) .or. (.not. (z <= 1.2d-105))) then
        tmp = (((t * a) / c) * (-4.0d0)) + (b / (z * c))
    else
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -1.1e-19) || !(z <= 1.2e-105)) {
		tmp = (((t * a) / c) * -4.0) + (b / (z * c));
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -1.1e-19) or not (z <= 1.2e-105):
		tmp = (((t * a) / c) * -4.0) + (b / (z * c))
	else:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -1.1e-19) || !(z <= 1.2e-105))
		tmp = Float64(Float64(Float64(Float64(t * a) / c) * -4.0) + Float64(b / Float64(z * c)));
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -1.1e-19) || ~((z <= 1.2e-105)))
		tmp = (((t * a) / c) * -4.0) + (b / (z * c));
	else
		tmp = (b + (9.0 * (x * y))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -1.1e-19], N[Not[LessEqual[z, 1.2e-105]], $MachinePrecision]], N[(N[(N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0999999999999999e-19 or 1.20000000000000007e-105 < z

   1. Initial program 68.4%

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

      1. associate-+l- 68.4%

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

      2. *-commutative 68.4%

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

      3. associate-*r* 65.9%

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

      4. *-commutative 65.9%

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

      5. associate-+l- 65.9%

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

   3. Simplified 70.5%

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

   4. Taylor expanded in x around 0 55.7%

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

      1. associate-*r* 57.2%

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

      2. *-commutative 57.2%

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

      3. associate-*l* 57.2%

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

      4. *-commutative 57.2%

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

      5. associate-*l* 57.2%

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

      6. *-rgt-identity 57.2%

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

      7. cancel-sign-sub-inv 57.2%

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

      8. *-rgt-identity 57.2%

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

      9. *-commutative 57.2%

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

      10. distribute-rgt-neg-in 57.2%

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

      11. *-commutative 57.2%

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

      12. distribute-rgt-neg-in 57.2%

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

      13. metadata-eval 57.2%

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

      14. *-commutative 57.2%

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

   6. Simplified 57.2%

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

   7. Taylor expanded in b around 0 70.6%

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

   if -1.0999999999999999e-19 < z < 1.20000000000000007e-105

   1. Initial program 95.3%

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

      1. associate-+l- 95.3%

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

      2. *-commutative 95.3%

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

      3. associate-*r* 94.4%

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

      4. *-commutative 94.4%

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

      5. associate-+l- 94.4%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in x around inf 85.9%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-19} \lor \neg \left(z \leq 1.2 \cdot 10^{-105}\right):\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4 + \frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 11: 49.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;b \leq -1.45 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-233}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-17}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{+60}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (/ b c) z)))
   (if (<= b -1.45e+16)
     t_1
     (if (<= b 5.2e-233)
       (* a (* t (/ -4.0 c)))
       (if (<= b 2.3e-17)
         (* 9.0 (* (/ x c) (/ y z)))
         (if (<= b 3.9e+60) (* (/ (* t a) c) -4.0) t_1))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double tmp;
	if (b <= -1.45e+16) {
		tmp = t_1;
	} else if (b <= 5.2e-233) {
		tmp = a * (t * (-4.0 / c));
	} else if (b <= 2.3e-17) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (b <= 3.9e+60) {
		tmp = ((t * a) / c) * -4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b / c) / z
    if (b <= (-1.45d+16)) then
        tmp = t_1
    else if (b <= 5.2d-233) then
        tmp = a * (t * ((-4.0d0) / c))
    else if (b <= 2.3d-17) then
        tmp = 9.0d0 * ((x / c) * (y / z))
    else if (b <= 3.9d+60) then
        tmp = ((t * a) / c) * (-4.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double tmp;
	if (b <= -1.45e+16) {
		tmp = t_1;
	} else if (b <= 5.2e-233) {
		tmp = a * (t * (-4.0 / c));
	} else if (b <= 2.3e-17) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (b <= 3.9e+60) {
		tmp = ((t * a) / c) * -4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (b / c) / z
	tmp = 0
	if b <= -1.45e+16:
		tmp = t_1
	elif b <= 5.2e-233:
		tmp = a * (t * (-4.0 / c))
	elif b <= 2.3e-17:
		tmp = 9.0 * ((x / c) * (y / z))
	elif b <= 3.9e+60:
		tmp = ((t * a) / c) * -4.0
	else:
		tmp = t_1
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b / c) / z)
	tmp = 0.0
	if (b <= -1.45e+16)
		tmp = t_1;
	elseif (b <= 5.2e-233)
		tmp = Float64(a * Float64(t * Float64(-4.0 / c)));
	elseif (b <= 2.3e-17)
		tmp = Float64(9.0 * Float64(Float64(x / c) * Float64(y / z)));
	elseif (b <= 3.9e+60)
		tmp = Float64(Float64(Float64(t * a) / c) * -4.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b / c) / z;
	tmp = 0.0;
	if (b <= -1.45e+16)
		tmp = t_1;
	elseif (b <= 5.2e-233)
		tmp = a * (t * (-4.0 / c));
	elseif (b <= 2.3e-17)
		tmp = 9.0 * ((x / c) * (y / z));
	elseif (b <= 3.9e+60)
		tmp = ((t * a) / c) * -4.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[b, -1.45e+16], t$95$1, If[LessEqual[b, 5.2e-233], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e-17], N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.9e+60], N[(N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.45e16 or 3.9000000000000003e60 < b

   1. Initial program 83.8%

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

      1. associate-+l- 83.8%

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

      2. *-commutative 83.8%

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

      3. associate-*r* 84.0%

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

      4. *-commutative 84.0%

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

      5. associate-+l- 84.0%

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

   3. Simplified 86.4%

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

   4. Taylor expanded in b around inf 50.8%

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

      1. associate-/r* 59.1%

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

   6. Simplified 59.1%

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

   if -1.45e16 < b < 5.1999999999999996e-233

   1. Initial program 72.4%

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

      1. associate-+l- 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-*r* 70.1%

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

      4. *-commutative 70.1%

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

      5. associate-+l- 70.1%

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

   3. Simplified 71.4%

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

      1. *-un-lft-identity 71.4%

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

      2. times-frac 78.1%

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

      3. associate-+l- 78.1%

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

      4. associate-*r* 78.1%

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

      5. associate-+l- 78.1%

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

      6. associate-*l* 78.1%

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

      7. associate-*r* 78.2%

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

   5. Applied egg-rr 78.2%

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

      1. associate-*r/ 78.3%

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

   7. Applied egg-rr 78.3%

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

   8. Taylor expanded in z around inf 51.3%

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

      1. associate-*r/ 51.3%

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

      2. *-commutative 51.3%

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

      3. associate-*l/ 51.2%

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

      4. *-commutative 51.2%

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

      5. *-commutative 51.2%

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

      6. associate-*l* 51.2%

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

   10. Simplified 51.2%

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

   if 5.1999999999999996e-233 < b < 2.30000000000000009e-17

   1. Initial program 82.3%

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

      1. associate-+l- 82.3%

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

      2. *-commutative 82.3%

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

      3. associate-*r* 74.8%

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

      4. *-commutative 74.8%

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

      5. associate-+l- 74.8%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in x around inf 55.5%

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

      1. times-frac 63.2%

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

   6. Applied egg-rr 63.2%

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

   if 2.30000000000000009e-17 < b < 3.9000000000000003e60

   1. Initial program 76.6%

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

      1. associate-+l- 76.6%

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

      2. *-commutative 76.6%

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

      3. associate-*r* 76.3%

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

      4. *-commutative 76.3%

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

      5. associate-+l- 76.3%

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

   3. Simplified 76.6%

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

   4. Taylor expanded in z around inf 68.1%

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

      1. *-commutative 68.1%

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

   6. Simplified 68.1%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+16}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-233}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-17}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{+60}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 12: 49.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;b \leq -2.05 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-234}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-17}:\\ \;\;\;\;\frac{x \cdot 9}{z \cdot \frac{c}{y}}\\ \mathbf{elif}\;b \leq 1.38 \cdot 10^{+60}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (/ b c) z)))
   (if (<= b -2.05e+16)
     t_1
     (if (<= b 3.8e-234)
       (* a (* t (/ -4.0 c)))
       (if (<= b 1.7e-17)
         (/ (* x 9.0) (* z (/ c y)))
         (if (<= b 1.38e+60) (* (/ (* t a) c) -4.0) t_1))))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double tmp;
	if (b <= -2.05e+16) {
		tmp = t_1;
	} else if (b <= 3.8e-234) {
		tmp = a * (t * (-4.0 / c));
	} else if (b <= 1.7e-17) {
		tmp = (x * 9.0) / (z * (c / y));
	} else if (b <= 1.38e+60) {
		tmp = ((t * a) / c) * -4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b / c) / z
    if (b <= (-2.05d+16)) then
        tmp = t_1
    else if (b <= 3.8d-234) then
        tmp = a * (t * ((-4.0d0) / c))
    else if (b <= 1.7d-17) then
        tmp = (x * 9.0d0) / (z * (c / y))
    else if (b <= 1.38d+60) then
        tmp = ((t * a) / c) * (-4.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double tmp;
	if (b <= -2.05e+16) {
		tmp = t_1;
	} else if (b <= 3.8e-234) {
		tmp = a * (t * (-4.0 / c));
	} else if (b <= 1.7e-17) {
		tmp = (x * 9.0) / (z * (c / y));
	} else if (b <= 1.38e+60) {
		tmp = ((t * a) / c) * -4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (b / c) / z
	tmp = 0
	if b <= -2.05e+16:
		tmp = t_1
	elif b <= 3.8e-234:
		tmp = a * (t * (-4.0 / c))
	elif b <= 1.7e-17:
		tmp = (x * 9.0) / (z * (c / y))
	elif b <= 1.38e+60:
		tmp = ((t * a) / c) * -4.0
	else:
		tmp = t_1
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b / c) / z)
	tmp = 0.0
	if (b <= -2.05e+16)
		tmp = t_1;
	elseif (b <= 3.8e-234)
		tmp = Float64(a * Float64(t * Float64(-4.0 / c)));
	elseif (b <= 1.7e-17)
		tmp = Float64(Float64(x * 9.0) / Float64(z * Float64(c / y)));
	elseif (b <= 1.38e+60)
		tmp = Float64(Float64(Float64(t * a) / c) * -4.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b / c) / z;
	tmp = 0.0;
	if (b <= -2.05e+16)
		tmp = t_1;
	elseif (b <= 3.8e-234)
		tmp = a * (t * (-4.0 / c));
	elseif (b <= 1.7e-17)
		tmp = (x * 9.0) / (z * (c / y));
	elseif (b <= 1.38e+60)
		tmp = ((t * a) / c) * -4.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[b, -2.05e+16], t$95$1, If[LessEqual[b, 3.8e-234], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e-17], N[(N[(x * 9.0), $MachinePrecision] / N[(z * N[(c / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.38e+60], N[(N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.05e16 or 1.38e60 < b

   1. Initial program 83.8%

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

      1. associate-+l- 83.8%

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

      2. *-commutative 83.8%

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

      3. associate-*r* 84.0%

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

      4. *-commutative 84.0%

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

      5. associate-+l- 84.0%

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

   3. Simplified 86.4%

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

   4. Taylor expanded in b around inf 50.8%

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

      1. associate-/r* 59.1%

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

   6. Simplified 59.1%

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

   if -2.05e16 < b < 3.79999999999999984e-234

   1. Initial program 72.4%

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

      1. associate-+l- 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-*r* 70.1%

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

      4. *-commutative 70.1%

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

      5. associate-+l- 70.1%

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

   3. Simplified 71.4%

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

      1. *-un-lft-identity 71.4%

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

      2. times-frac 78.1%

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

      3. associate-+l- 78.1%

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

      4. associate-*r* 78.1%

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

      5. associate-+l- 78.1%

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

      6. associate-*l* 78.1%

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

      7. associate-*r* 78.2%

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

   5. Applied egg-rr 78.2%

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

      1. associate-*r/ 78.3%

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

   7. Applied egg-rr 78.3%

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

   8. Taylor expanded in z around inf 51.3%

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

      1. associate-*r/ 51.3%

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

      2. *-commutative 51.3%

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

      3. associate-*l/ 51.2%

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

      4. *-commutative 51.2%

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

      5. *-commutative 51.2%

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

      6. associate-*l* 51.2%

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

   10. Simplified 51.2%

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

   if 3.79999999999999984e-234 < b < 1.6999999999999999e-17

   1. Initial program 82.3%

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

      1. associate-+l- 82.3%

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

      2. *-commutative 82.3%

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

      3. associate-*r* 74.8%

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

      4. *-commutative 74.8%

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

      5. associate-+l- 74.8%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in x around inf 55.5%

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

      1. associate-*r/ 55.5%

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

      2. associate-*r* 55.5%

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

      3. *-commutative 55.5%

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

      4. associate-*r* 55.5%

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

      5. *-commutative 55.5%

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

      6. times-frac 63.1%

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

      7. associate-/l* 63.0%

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

   6. Simplified 63.0%

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

      1. frac-times 58.4%

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

   8. Applied egg-rr 58.4%

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

   if 1.6999999999999999e-17 < b < 1.38e60

   1. Initial program 76.6%

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

      1. associate-+l- 76.6%

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

      2. *-commutative 76.6%

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

      3. associate-*r* 76.3%

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

      4. *-commutative 76.3%

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

      5. associate-+l- 76.3%

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

   3. Simplified 76.6%

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

   4. Taylor expanded in z around inf 68.1%

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

      1. *-commutative 68.1%

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

   6. Simplified 68.1%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.05 \cdot 10^{+16}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-234}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-17}:\\ \;\;\;\;\frac{x \cdot 9}{z \cdot \frac{c}{y}}\\ \mathbf{elif}\;b \leq 1.38 \cdot 10^{+60}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 13: 68.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+21} \lor \neg \left(z \leq 1.05 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -4e+21) (not (<= z 1.05e+60)))
   (* (/ (* t a) c) -4.0)
   (/ (+ b (* 9.0 (* x y))) (* z c))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -4e+21) || !(z <= 1.05e+60)) {
		tmp = ((t * a) / c) * -4.0;
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-4d+21)) .or. (.not. (z <= 1.05d+60))) then
        tmp = ((t * a) / c) * (-4.0d0)
    else
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -4e+21) || !(z <= 1.05e+60)) {
		tmp = ((t * a) / c) * -4.0;
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -4e+21) or not (z <= 1.05e+60):
		tmp = ((t * a) / c) * -4.0
	else:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -4e+21) || !(z <= 1.05e+60))
		tmp = Float64(Float64(Float64(t * a) / c) * -4.0);
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -4e+21) || ~((z <= 1.05e+60)))
		tmp = ((t * a) / c) * -4.0;
	else
		tmp = (b + (9.0 * (x * y))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -4e+21], N[Not[LessEqual[z, 1.05e+60]], $MachinePrecision]], N[(N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision], N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4e21 or 1.0500000000000001e60 < z

   1. Initial program 60.1%

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

      1. associate-+l- 60.1%

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

      2. *-commutative 60.1%

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

      3. associate-*r* 56.8%

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

      4. *-commutative 56.8%

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

      5. associate-+l- 56.8%

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

   3. Simplified 63.7%

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

   4. Taylor expanded in z around inf 62.0%

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

      1. *-commutative 62.0%

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

   6. Simplified 62.0%

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

   if -4e21 < z < 1.0500000000000001e60

   1. Initial program 95.0%

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

      1. associate-+l- 95.0%

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

      2. *-commutative 95.0%

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

      3. associate-*r* 94.3%

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

      4. *-commutative 94.3%

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

      5. associate-+l- 94.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in x around inf 78.0%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+21} \lor \neg \left(z \leq 1.05 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 14: 49.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;b \leq -33000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.75 \cdot 10^{-17}:\\ \;\;\;\;9 \cdot \frac{y \cdot \frac{x}{c}}{z}\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+59}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (/ b c) z)))
   (if (<= b -33000000000000.0)
     t_1
     (if (<= b 2.75e-17)
       (* 9.0 (/ (* y (/ x c)) z))
       (if (<= b 4.2e+59) (* (/ (* t a) c) -4.0) t_1)))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double tmp;
	if (b <= -33000000000000.0) {
		tmp = t_1;
	} else if (b <= 2.75e-17) {
		tmp = 9.0 * ((y * (x / c)) / z);
	} else if (b <= 4.2e+59) {
		tmp = ((t * a) / c) * -4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b / c) / z
    if (b <= (-33000000000000.0d0)) then
        tmp = t_1
    else if (b <= 2.75d-17) then
        tmp = 9.0d0 * ((y * (x / c)) / z)
    else if (b <= 4.2d+59) then
        tmp = ((t * a) / c) * (-4.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double tmp;
	if (b <= -33000000000000.0) {
		tmp = t_1;
	} else if (b <= 2.75e-17) {
		tmp = 9.0 * ((y * (x / c)) / z);
	} else if (b <= 4.2e+59) {
		tmp = ((t * a) / c) * -4.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (b / c) / z
	tmp = 0
	if b <= -33000000000000.0:
		tmp = t_1
	elif b <= 2.75e-17:
		tmp = 9.0 * ((y * (x / c)) / z)
	elif b <= 4.2e+59:
		tmp = ((t * a) / c) * -4.0
	else:
		tmp = t_1
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b / c) / z)
	tmp = 0.0
	if (b <= -33000000000000.0)
		tmp = t_1;
	elseif (b <= 2.75e-17)
		tmp = Float64(9.0 * Float64(Float64(y * Float64(x / c)) / z));
	elseif (b <= 4.2e+59)
		tmp = Float64(Float64(Float64(t * a) / c) * -4.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b / c) / z;
	tmp = 0.0;
	if (b <= -33000000000000.0)
		tmp = t_1;
	elseif (b <= 2.75e-17)
		tmp = 9.0 * ((y * (x / c)) / z);
	elseif (b <= 4.2e+59)
		tmp = ((t * a) / c) * -4.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[b, -33000000000000.0], t$95$1, If[LessEqual[b, 2.75e-17], N[(9.0 * N[(N[(y * N[(x / c), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.2e+59], N[(N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.3e13 or 4.19999999999999968e59 < b

   1. Initial program 84.0%

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

      1. associate-+l- 84.0%

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

      2. *-commutative 84.0%

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

      3. associate-*r* 84.1%

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

      4. *-commutative 84.1%

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

      5. associate-+l- 84.1%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in b around inf 50.3%

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

      1. associate-/r* 58.6%

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

   6. Simplified 58.6%

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

   if -3.3e13 < b < 2.75e-17

   1. Initial program 75.3%

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

      1. associate-+l- 75.3%

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

      2. *-commutative 75.3%

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

      3. associate-*r* 71.4%

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

      4. *-commutative 71.4%

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

      5. associate-+l- 71.4%

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

   3. Simplified 73.1%

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

   4. Taylor expanded in x around inf 46.3%

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

      1. times-frac 49.3%

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

   6. Applied egg-rr 49.3%

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

      1. associate-*r/ 52.4%

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

   8. Applied egg-rr 52.4%

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

   if 2.75e-17 < b < 4.19999999999999968e59

   1. Initial program 76.6%

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

      1. associate-+l- 76.6%

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

      2. *-commutative 76.6%

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

      3. associate-*r* 76.3%

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

      4. *-commutative 76.3%

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

      5. associate-+l- 76.3%

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

   3. Simplified 76.6%

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

   4. Taylor expanded in z around inf 68.1%

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

      1. *-commutative 68.1%

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

   6. Simplified 68.1%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -33000000000000:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 2.75 \cdot 10^{-17}:\\ \;\;\;\;9 \cdot \frac{y \cdot \frac{x}{c}}{z}\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+59}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 15: 50.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+16} \lor \neg \left(b \leq 10^{+55}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -1.65e+16) (not (<= b 1e+55)))
   (/ (/ b c) z)
   (* a (* t (/ -4.0 c)))))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1.65e+16) || !(b <= 1e+55)) {
		tmp = (b / c) / z;
	} else {
		tmp = a * (t * (-4.0 / c));
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-1.65d+16)) .or. (.not. (b <= 1d+55))) then
        tmp = (b / c) / z
    else
        tmp = a * (t * ((-4.0d0) / c))
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1.65e+16) || !(b <= 1e+55)) {
		tmp = (b / c) / z;
	} else {
		tmp = a * (t * (-4.0 / c));
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -1.65e+16) or not (b <= 1e+55):
		tmp = (b / c) / z
	else:
		tmp = a * (t * (-4.0 / c))
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -1.65e+16) || !(b <= 1e+55))
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(a * Float64(t * Float64(-4.0 / c)));
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -1.65e+16) || ~((b <= 1e+55)))
		tmp = (b / c) / z;
	else
		tmp = a * (t * (-4.0 / c));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -1.65e+16], N[Not[LessEqual[b, 1e+55]], $MachinePrecision]], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.65e16 or 1.00000000000000001e55 < b

   1. Initial program 83.8%

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

      1. associate-+l- 83.8%

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

      2. *-commutative 83.8%

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

      3. associate-*r* 84.0%

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

      4. *-commutative 84.0%

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

      5. associate-+l- 84.0%

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

   3. Simplified 86.4%

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

   4. Taylor expanded in b around inf 50.8%

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

      1. associate-/r* 59.1%

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

   6. Simplified 59.1%

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

   if -1.65e16 < b < 1.00000000000000001e55

   1. Initial program 75.7%

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

      1. associate-+l- 75.7%

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

      2. *-commutative 75.7%

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

      3. associate-*r* 72.1%

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

      4. *-commutative 72.1%

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

      5. associate-+l- 72.1%

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

   3. Simplified 73.7%

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

      1. *-un-lft-identity 73.7%

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

      2. times-frac 80.5%

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

      3. associate-+l- 80.5%

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

      4. associate-*r* 81.1%

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

      5. associate-+l- 81.1%

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

      6. associate-*l* 81.1%

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

      7. associate-*r* 80.5%

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

   5. Applied egg-rr 80.5%

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

      1. associate-*r/ 79.3%

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

   7. Applied egg-rr 79.3%

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

   8. Taylor expanded in z around inf 50.4%

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

      1. associate-*r/ 50.4%

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

      2. *-commutative 50.4%

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

      3. associate-*l/ 50.3%

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

      4. *-commutative 50.3%

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

      5. *-commutative 50.3%

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

      6. associate-*l* 50.1%

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

   10. Simplified 50.1%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+16} \lor \neg \left(b \leq 10^{+55}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \]

Alternative 16: 50.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -2.05 \cdot 10^{+16} \lor \neg \left(b \leq 1.48 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \end{array} \end{array} \]

FPCore

NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -2.05e+16) (not (<= b 1.48e+57)))
   (/ (/ b c) z)
   (* (/ (* t a) c) -4.0)))

C

assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -2.05e+16) || !(b <= 1.48e+57)) {
		tmp = (b / c) / z;
	} else {
		tmp = ((t * a) / c) * -4.0;
	}
	return tmp;
}

Fortran

NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-2.05d+16)) .or. (.not. (b <= 1.48d+57))) then
        tmp = (b / c) / z
    else
        tmp = ((t * a) / c) * (-4.0d0)
    end if
    code = tmp
end function

Java

assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -2.05e+16) || !(b <= 1.48e+57)) {
		tmp = (b / c) / z;
	} else {
		tmp = ((t * a) / c) * -4.0;
	}
	return tmp;
}

Python

[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -2.05e+16) or not (b <= 1.48e+57):
		tmp = (b / c) / z
	else:
		tmp = ((t * a) / c) * -4.0
	return tmp

Julia

t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -2.05e+16) || !(b <= 1.48e+57))
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(Float64(Float64(t * a) / c) * -4.0);
	end
	return tmp
end

MATLAB

t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -2.05e+16) || ~((b <= 1.48e+57)))
		tmp = (b / c) / z;
	else
		tmp = ((t * a) / c) * -4.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -2.05e+16], N[Not[LessEqual[b, 1.48e+57]], $MachinePrecision]], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(N[(t * a), $MachinePrecision] / c), $MachinePrecision] * -4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.05e16 or 1.47999999999999999e57 < b

   1. Initial program 83.8%

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

      1. associate-+l- 83.8%

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

      2. *-commutative 83.8%

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

      3. associate-*r* 84.0%

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

      4. *-commutative 84.0%

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

      5. associate-+l- 84.0%

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

   3. Simplified 86.4%

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

   4. Taylor expanded in b around inf 50.8%

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

      1. associate-/r* 59.1%

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

   6. Simplified 59.1%

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

   if -2.05e16 < b < 1.47999999999999999e57

   1. Initial program 75.7%

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

      1. associate-+l- 75.7%

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

      2. *-commutative 75.7%

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

      3. associate-*r* 72.1%

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

      4. *-commutative 72.1%

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

      5. associate-+l- 72.1%

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

   3. Simplified 73.7%

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

   4. Taylor expanded in z around inf 50.4%

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

      1. *-commutative 50.4%

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

   6. Simplified 50.4%

      \[\leadsto \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.05 \cdot 10^{+16} \lor \neg \left(b \leq 1.48 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot a}{c} \cdot -4\\ \end{array} \]

Alternative 17: 34.6% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.3%

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

   1. associate-+l- 79.3%

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

   2. associate-*l* 79.4%

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

   3. fma-neg 80.1%

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

   4. neg-sub0 80.1%

      \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{0 - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}\right)}{z \cdot c} \]

   5. associate-+l- 80.1%

      \[\leadsto \frac{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{\left(0 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}\right)}{z \cdot c} \]

   6. neg-sub0 80.1%

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

   7. +-commutative 80.1%

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

   8. distribute-rgt-neg-out 80.1%

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

   9. *-commutative 80.1%

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

   10. associate-*l* 78.2%

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

   11. distribute-rgt-neg-in 78.2%

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

   12. *-commutative 78.2%

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

   13. distribute-rgt-neg-in 78.2%

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

   14. distribute-rgt-neg-in 78.2%

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

   15. metadata-eval 78.2%

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

3. Simplified 78.2%

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

4. Taylor expanded in b around inf 29.4%

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

5. Final simplification 29.4%

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

Alternative 18: 33.8% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.3%

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

   1. associate-+l- 79.3%

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

   2. *-commutative 79.3%

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

   3. associate-*r* 77.4%

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

   4. *-commutative 77.4%

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

   5. associate-+l- 77.4%

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

3. Simplified 79.4%

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

4. Taylor expanded in b around inf 29.4%

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

   1. associate-/r* 32.4%

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

6. Simplified 32.4%

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

7. Final simplification 32.4%

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

Developer target: 81.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{c \cdot z}\\ t_2 := 4 \cdot \frac{a \cdot t}{c}\\ t_3 := \left(x \cdot 9\right) \cdot y\\ t_4 := \left(t_3 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b\\ t_5 := \frac{t_4}{z \cdot c}\\ t_6 := \frac{\left(t_3 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t_5 < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 < 0:\\ \;\;\;\;\frac{\frac{t_4}{z}}{c}\\ \mathbf{elif}\;t_5 < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t_5 < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + t_1\right) - t_2\\ \mathbf{elif}\;t_5 < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + t_1\right) - t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ b (* c z)))
        (t_2 (* 4.0 (/ (* a t) c)))
        (t_3 (* (* x 9.0) y))
        (t_4 (+ (- t_3 (* (* (* z 4.0) t) a)) b))
        (t_5 (/ t_4 (* z c)))
        (t_6 (/ (+ (- t_3 (* (* z 4.0) (* t a))) b) (* z c))))
   (if (< t_5 -1.100156740804105e-171)
     t_6
     (if (< t_5 0.0)
       (/ (/ t_4 z) c)
       (if (< t_5 1.1708877911747488e-53)
         t_6
         (if (< t_5 2.876823679546137e+130)
           (- (+ (* (* 9.0 (/ y c)) (/ x z)) t_1) t_2)
           (if (< t_5 1.3838515042456319e+158)
             t_6
             (- (+ (* 9.0 (* (/ y (* c z)) x)) t_1) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_1 = b / (c * z)
    t_2 = 4.0d0 * ((a * t) / c)
    t_3 = (x * 9.0d0) * y
    t_4 = (t_3 - (((z * 4.0d0) * t) * a)) + b
    t_5 = t_4 / (z * c)
    t_6 = ((t_3 - ((z * 4.0d0) * (t * a))) + b) / (z * c)
    if (t_5 < (-1.100156740804105d-171)) then
        tmp = t_6
    else if (t_5 < 0.0d0) then
        tmp = (t_4 / z) / c
    else if (t_5 < 1.1708877911747488d-53) then
        tmp = t_6
    else if (t_5 < 2.876823679546137d+130) then
        tmp = (((9.0d0 * (y / c)) * (x / z)) + t_1) - t_2
    else if (t_5 < 1.3838515042456319d+158) then
        tmp = t_6
    else
        tmp = ((9.0d0 * ((y / (c * z)) * x)) + t_1) - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = b / (c * z);
	double t_2 = 4.0 * ((a * t) / c);
	double t_3 = (x * 9.0) * y;
	double t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	double t_5 = t_4 / (z * c);
	double t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	double tmp;
	if (t_5 < -1.100156740804105e-171) {
		tmp = t_6;
	} else if (t_5 < 0.0) {
		tmp = (t_4 / z) / c;
	} else if (t_5 < 1.1708877911747488e-53) {
		tmp = t_6;
	} else if (t_5 < 2.876823679546137e+130) {
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	} else if (t_5 < 1.3838515042456319e+158) {
		tmp = t_6;
	} else {
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = b / (c * z)
	t_2 = 4.0 * ((a * t) / c)
	t_3 = (x * 9.0) * y
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b
	t_5 = t_4 / (z * c)
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c)
	tmp = 0
	if t_5 < -1.100156740804105e-171:
		tmp = t_6
	elif t_5 < 0.0:
		tmp = (t_4 / z) / c
	elif t_5 < 1.1708877911747488e-53:
		tmp = t_6
	elif t_5 < 2.876823679546137e+130:
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2
	elif t_5 < 1.3838515042456319e+158:
		tmp = t_6
	else:
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(b / Float64(c * z))
	t_2 = Float64(4.0 * Float64(Float64(a * t) / c))
	t_3 = Float64(Float64(x * 9.0) * y)
	t_4 = Float64(Float64(t_3 - Float64(Float64(Float64(z * 4.0) * t) * a)) + b)
	t_5 = Float64(t_4 / Float64(z * c))
	t_6 = Float64(Float64(Float64(t_3 - Float64(Float64(z * 4.0) * Float64(t * a))) + b) / Float64(z * c))
	tmp = 0.0
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = Float64(Float64(t_4 / z) / c);
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(y / c)) * Float64(x / z)) + t_1) - t_2);
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = Float64(Float64(Float64(9.0 * Float64(Float64(y / Float64(c * z)) * x)) + t_1) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = b / (c * z);
	t_2 = 4.0 * ((a * t) / c);
	t_3 = (x * 9.0) * y;
	t_4 = (t_3 - (((z * 4.0) * t) * a)) + b;
	t_5 = t_4 / (z * c);
	t_6 = ((t_3 - ((z * 4.0) * (t * a))) + b) / (z * c);
	tmp = 0.0;
	if (t_5 < -1.100156740804105e-171)
		tmp = t_6;
	elseif (t_5 < 0.0)
		tmp = (t_4 / z) / c;
	elseif (t_5 < 1.1708877911747488e-53)
		tmp = t_6;
	elseif (t_5 < 2.876823679546137e+130)
		tmp = (((9.0 * (y / c)) * (x / z)) + t_1) - t_2;
	elseif (t_5 < 1.3838515042456319e+158)
		tmp = t_6;
	else
		tmp = ((9.0 * ((y / (c * z)) * x)) + t_1) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(b / N[(c * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(4.0 * N[(N[(a * t), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$3 - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$5, -1.100156740804105e-171], t$95$6, If[Less[t$95$5, 0.0], N[(N[(t$95$4 / z), $MachinePrecision] / c), $MachinePrecision], If[Less[t$95$5, 1.1708877911747488e-53], t$95$6, If[Less[t$95$5, 2.876823679546137e+130], N[(N[(N[(N[(9.0 * N[(y / c), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[t$95$5, 1.3838515042456319e+158], t$95$6, N[(N[(N[(9.0 * N[(N[(y / N[(c * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]]]]]]]]

Reproduce

herbie shell --seed 2023285 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :herbie-target
  (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) -1.100156740804105e-171) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 0.0) (/ (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.1708877911747488e-53) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 2.876823679546137e+130) (- (+ (* (* 9.0 (/ y c)) (/ x z)) (/ b (* c z))) (* 4.0 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.3838515042456319e+158) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (- (+ (* 9.0 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4.0 (/ (* a t) c))))))))

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