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

Percentage Accurate: 79.6% → 91.5%

Time: 19.1s

Alternatives: 21

Speedup: 0.9×

• 38.9% 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: 79.6% 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: 91.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\\ \mathbf{if}\;z \leq -1 \cdot 10^{-10}:\\ \;\;\;\;\frac{t_1 + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-45}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, t_1\right)}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (fma x (* 9.0 y) b) z)))
   (if (<= z -1e-10)
     (/ (+ t_1 (* t (* a -4.0))) c)
     (if (<= z 4.5e-45)
       (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))
       (/ (fma t (* a -4.0) t_1) c)))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma(x, (9.0 * y), b) / z;
	double tmp;
	if (z <= -1e-10) {
		tmp = (t_1 + (t * (a * -4.0))) / c;
	} else if (z <= 4.5e-45) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = fma(t, (a * -4.0), t_1) / c;
	}
	return tmp;
}

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(fma(x, Float64(9.0 * y), b) / z)
	tmp = 0.0
	if (z <= -1e-10)
		tmp = Float64(Float64(t_1 + Float64(t * Float64(a * -4.0))) / c);
	elseif (z <= 4.5e-45)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = Float64(fma(t, Float64(a * -4.0), t_1) / c);
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -1e-10], N[(N[(t$95$1 + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 4.5e-45], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(a * -4.0), $MachinePrecision] + t$95$1), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.00000000000000004e-10

   1. Initial program 64.3%

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

      1. associate-/r* 76.6%

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

   3. Simplified 87.7%

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

   if -1.00000000000000004e-10 < z < 4.4999999999999999e-45

   1. Initial program 98.8%

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

   if 4.4999999999999999e-45 < z

   1. Initial program 59.8%

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

      1. associate-/r* 70.7%

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

   3. Simplified 90.3%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-10}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-45}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \end{array} \]

Alternative 2: 91.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{-12}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t_1}{c}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-45}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + \frac{b + x \cdot \left(9 \cdot y\right)}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))))
   (if (<= z -7.2e-12)
     (/ (+ (/ (fma x (* 9.0 y) b) z) t_1) c)
     (if (<= z 4.5e-45)
       (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))
       (/ (+ t_1 (/ (+ b (* x (* 9.0 y))) z)) c)))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (z <= -7.2e-12) {
		tmp = ((fma(x, (9.0 * y), b) / z) + t_1) / c;
	} else if (z <= 4.5e-45) {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	} else {
		tmp = (t_1 + ((b + (x * (9.0 * y))) / z)) / c;
	}
	return tmp;
}

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (z <= -7.2e-12)
		tmp = Float64(Float64(Float64(fma(x, Float64(9.0 * y), b) / z) + t_1) / c);
	elseif (z <= 4.5e-45)
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	else
		tmp = Float64(Float64(t_1 + Float64(Float64(b + Float64(x * Float64(9.0 * y))) / z)) / c);
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.2e-12], N[(N[(N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision] + t$95$1), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 4.5e-45], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 + N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.2e-12

   1. Initial program 64.3%

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

      1. associate-/r* 76.6%

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

   3. Simplified 87.7%

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

   if -7.2e-12 < z < 4.4999999999999999e-45

   1. Initial program 98.8%

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

   if 4.4999999999999999e-45 < z

   1. Initial program 59.8%

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

      1. associate-/r* 70.7%

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

   3. Simplified 90.3%

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

      1. fma-udef 90.3%

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

   5. Applied egg-rr 90.3%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-12}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-45}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b + x \cdot \left(9 \cdot y\right)}{z}}{c}\\ \end{array} \]

Alternative 3: 49.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot -4}{\frac{c}{a}}\\ t_2 := \frac{\frac{b}{c}}{z}\\ t_3 := 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{if}\;b \leq -6 \cdot 10^{+72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 10^{-238}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{-76}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right)}{c}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-6}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.28 \cdot 10^{+203}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* t -4.0) (/ c a)))
        (t_2 (/ (/ b c) z))
        (t_3 (* 9.0 (* (/ y c) (/ x z)))))
   (if (<= b -6e+72)
     t_2
     (if (<= b -6e-302)
       t_1
       (if (<= b 1e-238)
         t_3
         (if (<= b 2.55e-76)
           (/ (* a (* t -4.0)) c)
           (if (<= b 7e-6)
             (* 9.0 (* (/ x c) (/ y z)))
             (if (<= b 1.6e+96) t_1 (if (<= b 1.28e+203) t_3 t_2)))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (t * -4.0) / (c / a);
	double t_2 = (b / c) / z;
	double t_3 = 9.0 * ((y / c) * (x / z));
	double tmp;
	if (b <= -6e+72) {
		tmp = t_2;
	} else if (b <= -6e-302) {
		tmp = t_1;
	} else if (b <= 1e-238) {
		tmp = t_3;
	} else if (b <= 2.55e-76) {
		tmp = (a * (t * -4.0)) / c;
	} else if (b <= 7e-6) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (b <= 1.6e+96) {
		tmp = t_1;
	} else if (b <= 1.28e+203) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (t * (-4.0d0)) / (c / a)
    t_2 = (b / c) / z
    t_3 = 9.0d0 * ((y / c) * (x / z))
    if (b <= (-6d+72)) then
        tmp = t_2
    else if (b <= (-6d-302)) then
        tmp = t_1
    else if (b <= 1d-238) then
        tmp = t_3
    else if (b <= 2.55d-76) then
        tmp = (a * (t * (-4.0d0))) / c
    else if (b <= 7d-6) then
        tmp = 9.0d0 * ((x / c) * (y / z))
    else if (b <= 1.6d+96) then
        tmp = t_1
    else if (b <= 1.28d+203) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (t * -4.0) / (c / a);
	double t_2 = (b / c) / z;
	double t_3 = 9.0 * ((y / c) * (x / z));
	double tmp;
	if (b <= -6e+72) {
		tmp = t_2;
	} else if (b <= -6e-302) {
		tmp = t_1;
	} else if (b <= 1e-238) {
		tmp = t_3;
	} else if (b <= 2.55e-76) {
		tmp = (a * (t * -4.0)) / c;
	} else if (b <= 7e-6) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (b <= 1.6e+96) {
		tmp = t_1;
	} else if (b <= 1.28e+203) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (t * -4.0) / (c / a)
	t_2 = (b / c) / z
	t_3 = 9.0 * ((y / c) * (x / z))
	tmp = 0
	if b <= -6e+72:
		tmp = t_2
	elif b <= -6e-302:
		tmp = t_1
	elif b <= 1e-238:
		tmp = t_3
	elif b <= 2.55e-76:
		tmp = (a * (t * -4.0)) / c
	elif b <= 7e-6:
		tmp = 9.0 * ((x / c) * (y / z))
	elif b <= 1.6e+96:
		tmp = t_1
	elif b <= 1.28e+203:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(t * -4.0) / Float64(c / a))
	t_2 = Float64(Float64(b / c) / z)
	t_3 = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)))
	tmp = 0.0
	if (b <= -6e+72)
		tmp = t_2;
	elseif (b <= -6e-302)
		tmp = t_1;
	elseif (b <= 1e-238)
		tmp = t_3;
	elseif (b <= 2.55e-76)
		tmp = Float64(Float64(a * Float64(t * -4.0)) / c);
	elseif (b <= 7e-6)
		tmp = Float64(9.0 * Float64(Float64(x / c) * Float64(y / z)));
	elseif (b <= 1.6e+96)
		tmp = t_1;
	elseif (b <= 1.28e+203)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (t * -4.0) / (c / a);
	t_2 = (b / c) / z;
	t_3 = 9.0 * ((y / c) * (x / z));
	tmp = 0.0;
	if (b <= -6e+72)
		tmp = t_2;
	elseif (b <= -6e-302)
		tmp = t_1;
	elseif (b <= 1e-238)
		tmp = t_3;
	elseif (b <= 2.55e-76)
		tmp = (a * (t * -4.0)) / c;
	elseif (b <= 7e-6)
		tmp = 9.0 * ((x / c) * (y / z));
	elseif (b <= 1.6e+96)
		tmp = t_1;
	elseif (b <= 1.28e+203)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(t * -4.0), $MachinePrecision] / N[(c / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$3 = N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6e+72], t$95$2, If[LessEqual[b, -6e-302], t$95$1, If[LessEqual[b, 1e-238], t$95$3, If[LessEqual[b, 2.55e-76], N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[b, 7e-6], N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.6e+96], t$95$1, If[LessEqual[b, 1.28e+203], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -6.00000000000000006e72 or 1.28000000000000005e203 < b

   1. Initial program 77.9%

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

      1. associate-*l* 77.9%

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

      2. associate-*l* 76.7%

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

   3. Simplified 76.7%

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

   4. Taylor expanded in b around inf 56.9%

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

      1. associate-/r* 65.9%

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

   6. Simplified 65.9%

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

   if -6.00000000000000006e72 < b < -5.99999999999999978e-302 or 6.99999999999999989e-6 < b < 1.60000000000000003e96

   1. Initial program 74.8%

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

      1. associate-*l* 74.8%

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

      2. associate-*l* 78.0%

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

   3. Simplified 78.0%

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

      1. *-un-lft-identity 78.0%

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

      2. *-commutative 78.0%

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

      3. times-frac 80.4%

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

   5. Applied egg-rr 80.4%

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

   6. Taylor expanded in z around inf 56.5%

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

      1. associate-*r/ 55.5%

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

      2. *-commutative 55.5%

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

      3. associate-*r* 55.5%

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

      4. *-commutative 55.5%

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

      5. associate-/l* 60.3%

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

   8. Simplified 60.3%

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

   if -5.99999999999999978e-302 < b < 9.9999999999999999e-239 or 1.60000000000000003e96 < b < 1.28000000000000005e203

   1. Initial program 67.8%

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

      1. associate-/r* 75.6%

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

   3. Simplified 81.2%

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

      1. fma-udef 81.2%

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

   5. Applied egg-rr 81.2%

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

   6. Taylor expanded in x around inf 46.2%

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

      1. times-frac 65.2%

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

   8. Simplified 65.2%

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

   if 9.9999999999999999e-239 < b < 2.54999999999999993e-76

   1. Initial program 84.6%

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

      1. associate-/r* 87.5%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in z around inf 79.0%

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

      1. *-commutative 79.0%

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

      2. *-commutative 79.0%

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

      3. *-commutative 79.0%

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

      4. associate-*l* 79.0%

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

   6. Simplified 79.0%

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

   if 2.54999999999999993e-76 < b < 6.99999999999999989e-6

   1. Initial program 77.4%

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

      1. associate-/r* 77.4%

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

   3. Simplified 88.8%

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

      1. fma-udef 88.8%

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

   5. Applied egg-rr 88.8%

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

   6. Taylor expanded in x around inf 50.1%

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

      1. times-frac 61.0%

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

   8. Simplified 61.0%

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

      1. associate-*l/ 55.4%

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

   10. Applied egg-rr 55.4%

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

   11. Taylor expanded in y around 0 50.1%

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

       1. *-commutative 50.1%

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

       2. times-frac 60.3%

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

   13. Simplified 60.3%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+72}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-302}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq 10^{-238}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{-76}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right)}{c}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-6}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+96}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq 1.28 \cdot 10^{+203}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 4: 49.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot -4}{\frac{c}{a}}\\ t_2 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;b \leq -1.16 \cdot 10^{+73}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-241}:\\ \;\;\;\;9 \cdot \frac{y \cdot \frac{x}{z}}{c}\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-76}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right)}{c}\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-5}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+199}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* t -4.0) (/ c a))) (t_2 (/ (/ b c) z)))
   (if (<= b -1.16e+73)
     t_2
     (if (<= b -6.2e-302)
       t_1
       (if (<= b 9.2e-241)
         (* 9.0 (/ (* y (/ x z)) c))
         (if (<= b 2.2e-76)
           (/ (* a (* t -4.0)) c)
           (if (<= b 1.6e-5)
             (* 9.0 (* (/ x c) (/ y z)))
             (if (<= b 2.6e+96)
               t_1
               (if (<= b 1.15e+199) (* 9.0 (* (/ y c) (/ x z))) t_2)))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (t * -4.0) / (c / a);
	double t_2 = (b / c) / z;
	double tmp;
	if (b <= -1.16e+73) {
		tmp = t_2;
	} else if (b <= -6.2e-302) {
		tmp = t_1;
	} else if (b <= 9.2e-241) {
		tmp = 9.0 * ((y * (x / z)) / c);
	} else if (b <= 2.2e-76) {
		tmp = (a * (t * -4.0)) / c;
	} else if (b <= 1.6e-5) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (b <= 2.6e+96) {
		tmp = t_1;
	} else if (b <= 1.15e+199) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t * (-4.0d0)) / (c / a)
    t_2 = (b / c) / z
    if (b <= (-1.16d+73)) then
        tmp = t_2
    else if (b <= (-6.2d-302)) then
        tmp = t_1
    else if (b <= 9.2d-241) then
        tmp = 9.0d0 * ((y * (x / z)) / c)
    else if (b <= 2.2d-76) then
        tmp = (a * (t * (-4.0d0))) / c
    else if (b <= 1.6d-5) then
        tmp = 9.0d0 * ((x / c) * (y / z))
    else if (b <= 2.6d+96) then
        tmp = t_1
    else if (b <= 1.15d+199) then
        tmp = 9.0d0 * ((y / c) * (x / z))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (t * -4.0) / (c / a);
	double t_2 = (b / c) / z;
	double tmp;
	if (b <= -1.16e+73) {
		tmp = t_2;
	} else if (b <= -6.2e-302) {
		tmp = t_1;
	} else if (b <= 9.2e-241) {
		tmp = 9.0 * ((y * (x / z)) / c);
	} else if (b <= 2.2e-76) {
		tmp = (a * (t * -4.0)) / c;
	} else if (b <= 1.6e-5) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (b <= 2.6e+96) {
		tmp = t_1;
	} else if (b <= 1.15e+199) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (t * -4.0) / (c / a)
	t_2 = (b / c) / z
	tmp = 0
	if b <= -1.16e+73:
		tmp = t_2
	elif b <= -6.2e-302:
		tmp = t_1
	elif b <= 9.2e-241:
		tmp = 9.0 * ((y * (x / z)) / c)
	elif b <= 2.2e-76:
		tmp = (a * (t * -4.0)) / c
	elif b <= 1.6e-5:
		tmp = 9.0 * ((x / c) * (y / z))
	elif b <= 2.6e+96:
		tmp = t_1
	elif b <= 1.15e+199:
		tmp = 9.0 * ((y / c) * (x / z))
	else:
		tmp = t_2
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(t * -4.0) / Float64(c / a))
	t_2 = Float64(Float64(b / c) / z)
	tmp = 0.0
	if (b <= -1.16e+73)
		tmp = t_2;
	elseif (b <= -6.2e-302)
		tmp = t_1;
	elseif (b <= 9.2e-241)
		tmp = Float64(9.0 * Float64(Float64(y * Float64(x / z)) / c));
	elseif (b <= 2.2e-76)
		tmp = Float64(Float64(a * Float64(t * -4.0)) / c);
	elseif (b <= 1.6e-5)
		tmp = Float64(9.0 * Float64(Float64(x / c) * Float64(y / z)));
	elseif (b <= 2.6e+96)
		tmp = t_1;
	elseif (b <= 1.15e+199)
		tmp = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (t * -4.0) / (c / a);
	t_2 = (b / c) / z;
	tmp = 0.0;
	if (b <= -1.16e+73)
		tmp = t_2;
	elseif (b <= -6.2e-302)
		tmp = t_1;
	elseif (b <= 9.2e-241)
		tmp = 9.0 * ((y * (x / z)) / c);
	elseif (b <= 2.2e-76)
		tmp = (a * (t * -4.0)) / c;
	elseif (b <= 1.6e-5)
		tmp = 9.0 * ((x / c) * (y / z));
	elseif (b <= 2.6e+96)
		tmp = t_1;
	elseif (b <= 1.15e+199)
		tmp = 9.0 * ((y / c) * (x / z));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(t * -4.0), $MachinePrecision] / N[(c / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[b, -1.16e+73], t$95$2, If[LessEqual[b, -6.2e-302], t$95$1, If[LessEqual[b, 9.2e-241], N[(9.0 * N[(N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.2e-76], N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[b, 1.6e-5], N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.6e+96], t$95$1, If[LessEqual[b, 1.15e+199], N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -1.16000000000000007e73 or 1.14999999999999997e199 < b

   1. Initial program 77.9%

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

      1. associate-*l* 77.9%

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

      2. associate-*l* 76.7%

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

   3. Simplified 76.7%

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

   4. Taylor expanded in b around inf 56.9%

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

      1. associate-/r* 65.9%

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

   6. Simplified 65.9%

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

   if -1.16000000000000007e73 < b < -6.19999999999999967e-302 or 1.59999999999999993e-5 < b < 2.6e96

   1. Initial program 74.8%

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

      1. associate-*l* 74.8%

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

      2. associate-*l* 78.0%

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

   3. Simplified 78.0%

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

      1. *-un-lft-identity 78.0%

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

      2. *-commutative 78.0%

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

      3. times-frac 80.4%

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

   5. Applied egg-rr 80.4%

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

   6. Taylor expanded in z around inf 56.5%

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

      1. associate-*r/ 55.5%

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

      2. *-commutative 55.5%

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

      3. associate-*r* 55.5%

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

      4. *-commutative 55.5%

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

      5. associate-/l* 60.3%

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

   8. Simplified 60.3%

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

   if -6.19999999999999967e-302 < b < 9.1999999999999997e-241

   1. Initial program 59.8%

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

      1. associate-/r* 67.4%

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

   3. Simplified 67.6%

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

      1. fma-udef 67.6%

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

   5. Applied egg-rr 67.6%

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

   6. Taylor expanded in x around inf 51.1%

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

      1. times-frac 75.5%

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

   8. Simplified 75.5%

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

      1. associate-*l/ 75.3%

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

   10. Applied egg-rr 75.3%

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

   if 9.1999999999999997e-241 < b < 2.19999999999999999e-76

   1. Initial program 84.6%

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

      1. associate-/r* 87.5%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in z around inf 79.0%

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

      1. *-commutative 79.0%

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

      2. *-commutative 79.0%

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

      3. *-commutative 79.0%

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

      4. associate-*l* 79.0%

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

   6. Simplified 79.0%

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

   if 2.19999999999999999e-76 < b < 1.59999999999999993e-5

   1. Initial program 77.4%

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

      1. associate-/r* 77.4%

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

   3. Simplified 88.8%

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

      1. fma-udef 88.8%

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

   5. Applied egg-rr 88.8%

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

   6. Taylor expanded in x around inf 50.1%

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

      1. times-frac 61.0%

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

   8. Simplified 61.0%

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

      1. associate-*l/ 55.4%

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

   10. Applied egg-rr 55.4%

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

   11. Taylor expanded in y around 0 50.1%

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

       1. *-commutative 50.1%

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

       2. times-frac 60.3%

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

   13. Simplified 60.3%

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

   if 2.6e96 < b < 1.14999999999999997e199

   1. Initial program 71.8%

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

      1. associate-/r* 79.7%

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

   3. Simplified 88.0%

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

      1. fma-udef 88.0%

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

   5. Applied egg-rr 88.0%

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

   6. Taylor expanded in x around inf 43.7%

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

      1. times-frac 60.1%

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

   8. Simplified 60.1%

      \[\leadsto \color{blue}{9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.16 \cdot 10^{+73}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-302}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-241}:\\ \;\;\;\;9 \cdot \frac{y \cdot \frac{x}{z}}{c}\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-76}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right)}{c}\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-5}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+96}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+199}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 5: 48.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{if}\;b \leq -6 \cdot 10^{+72}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{-242}:\\ \;\;\;\;9 \cdot \frac{y \cdot \frac{x}{z}}{c}\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-77}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right)}{c}\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-7}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+220}:\\ \;\;\;\;\frac{9}{z} \cdot \frac{y}{\frac{c}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* t -4.0) (/ c a))))
   (if (<= b -6e+72)
     (/ (/ b c) z)
     (if (<= b -6.6e-302)
       t_1
       (if (<= b 6.6e-242)
         (* 9.0 (/ (* y (/ x z)) c))
         (if (<= b 3.8e-77)
           (/ (* a (* t -4.0)) c)
           (if (<= b 8e-7)
             (* 9.0 (* (/ x c) (/ y z)))
             (if (<= b 2.4e+96)
               t_1
               (if (<= b 1.7e+220)
                 (* (/ 9.0 z) (/ y (/ c x)))
                 (* (/ b z) (/ 1.0 c)))))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (t * -4.0) / (c / a);
	double tmp;
	if (b <= -6e+72) {
		tmp = (b / c) / z;
	} else if (b <= -6.6e-302) {
		tmp = t_1;
	} else if (b <= 6.6e-242) {
		tmp = 9.0 * ((y * (x / z)) / c);
	} else if (b <= 3.8e-77) {
		tmp = (a * (t * -4.0)) / c;
	} else if (b <= 8e-7) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (b <= 2.4e+96) {
		tmp = t_1;
	} else if (b <= 1.7e+220) {
		tmp = (9.0 / z) * (y / (c / x));
	} else {
		tmp = (b / z) * (1.0 / c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * (-4.0d0)) / (c / a)
    if (b <= (-6d+72)) then
        tmp = (b / c) / z
    else if (b <= (-6.6d-302)) then
        tmp = t_1
    else if (b <= 6.6d-242) then
        tmp = 9.0d0 * ((y * (x / z)) / c)
    else if (b <= 3.8d-77) then
        tmp = (a * (t * (-4.0d0))) / c
    else if (b <= 8d-7) then
        tmp = 9.0d0 * ((x / c) * (y / z))
    else if (b <= 2.4d+96) then
        tmp = t_1
    else if (b <= 1.7d+220) then
        tmp = (9.0d0 / z) * (y / (c / x))
    else
        tmp = (b / z) * (1.0d0 / c)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (t * -4.0) / (c / a);
	double tmp;
	if (b <= -6e+72) {
		tmp = (b / c) / z;
	} else if (b <= -6.6e-302) {
		tmp = t_1;
	} else if (b <= 6.6e-242) {
		tmp = 9.0 * ((y * (x / z)) / c);
	} else if (b <= 3.8e-77) {
		tmp = (a * (t * -4.0)) / c;
	} else if (b <= 8e-7) {
		tmp = 9.0 * ((x / c) * (y / z));
	} else if (b <= 2.4e+96) {
		tmp = t_1;
	} else if (b <= 1.7e+220) {
		tmp = (9.0 / z) * (y / (c / x));
	} else {
		tmp = (b / z) * (1.0 / c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (t * -4.0) / (c / a)
	tmp = 0
	if b <= -6e+72:
		tmp = (b / c) / z
	elif b <= -6.6e-302:
		tmp = t_1
	elif b <= 6.6e-242:
		tmp = 9.0 * ((y * (x / z)) / c)
	elif b <= 3.8e-77:
		tmp = (a * (t * -4.0)) / c
	elif b <= 8e-7:
		tmp = 9.0 * ((x / c) * (y / z))
	elif b <= 2.4e+96:
		tmp = t_1
	elif b <= 1.7e+220:
		tmp = (9.0 / z) * (y / (c / x))
	else:
		tmp = (b / z) * (1.0 / c)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(t * -4.0) / Float64(c / a))
	tmp = 0.0
	if (b <= -6e+72)
		tmp = Float64(Float64(b / c) / z);
	elseif (b <= -6.6e-302)
		tmp = t_1;
	elseif (b <= 6.6e-242)
		tmp = Float64(9.0 * Float64(Float64(y * Float64(x / z)) / c));
	elseif (b <= 3.8e-77)
		tmp = Float64(Float64(a * Float64(t * -4.0)) / c);
	elseif (b <= 8e-7)
		tmp = Float64(9.0 * Float64(Float64(x / c) * Float64(y / z)));
	elseif (b <= 2.4e+96)
		tmp = t_1;
	elseif (b <= 1.7e+220)
		tmp = Float64(Float64(9.0 / z) * Float64(y / Float64(c / x)));
	else
		tmp = Float64(Float64(b / z) * Float64(1.0 / c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (t * -4.0) / (c / a);
	tmp = 0.0;
	if (b <= -6e+72)
		tmp = (b / c) / z;
	elseif (b <= -6.6e-302)
		tmp = t_1;
	elseif (b <= 6.6e-242)
		tmp = 9.0 * ((y * (x / z)) / c);
	elseif (b <= 3.8e-77)
		tmp = (a * (t * -4.0)) / c;
	elseif (b <= 8e-7)
		tmp = 9.0 * ((x / c) * (y / z));
	elseif (b <= 2.4e+96)
		tmp = t_1;
	elseif (b <= 1.7e+220)
		tmp = (9.0 / z) * (y / (c / x));
	else
		tmp = (b / z) * (1.0 / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(t * -4.0), $MachinePrecision] / N[(c / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6e+72], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, -6.6e-302], t$95$1, If[LessEqual[b, 6.6e-242], N[(9.0 * N[(N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.8e-77], N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[b, 8e-7], N[(9.0 * N[(N[(x / c), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.4e+96], t$95$1, If[LessEqual[b, 1.7e+220], N[(N[(9.0 / z), $MachinePrecision] * N[(y / N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / z), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -6.00000000000000006e72

   1. Initial program 81.0%

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

      1. associate-*l* 81.0%

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

      2. associate-*l* 79.0%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in b around inf 58.1%

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

      1. associate-/r* 64.3%

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

   6. Simplified 64.3%

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

   if -6.00000000000000006e72 < b < -6.6000000000000005e-302 or 7.9999999999999996e-7 < b < 2.39999999999999993e96

   1. Initial program 74.8%

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

      1. associate-*l* 74.8%

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

      2. associate-*l* 78.0%

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

   3. Simplified 78.0%

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

      1. *-un-lft-identity 78.0%

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

      2. *-commutative 78.0%

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

      3. times-frac 80.4%

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

   5. Applied egg-rr 80.4%

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

   6. Taylor expanded in z around inf 56.5%

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

      1. associate-*r/ 55.5%

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

      2. *-commutative 55.5%

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

      3. associate-*r* 55.5%

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

      4. *-commutative 55.5%

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

      5. associate-/l* 60.3%

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

   8. Simplified 60.3%

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

   if -6.6000000000000005e-302 < b < 6.59999999999999963e-242

   1. Initial program 59.8%

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

      1. associate-/r* 67.4%

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

   3. Simplified 67.6%

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

      1. fma-udef 67.6%

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

   5. Applied egg-rr 67.6%

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

   6. Taylor expanded in x around inf 51.1%

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

      1. times-frac 75.5%

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

   8. Simplified 75.5%

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

      1. associate-*l/ 75.3%

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

   10. Applied egg-rr 75.3%

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

   if 6.59999999999999963e-242 < b < 3.7999999999999999e-77

   1. Initial program 84.6%

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

      1. associate-/r* 87.5%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in z around inf 79.0%

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

      1. *-commutative 79.0%

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

      2. *-commutative 79.0%

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

      3. *-commutative 79.0%

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

      4. associate-*l* 79.0%

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

   6. Simplified 79.0%

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

   if 3.7999999999999999e-77 < b < 7.9999999999999996e-7

   1. Initial program 77.4%

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

      1. associate-/r* 77.4%

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

   3. Simplified 88.8%

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

      1. fma-udef 88.8%

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

   5. Applied egg-rr 88.8%

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

   6. Taylor expanded in x around inf 50.1%

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

      1. times-frac 61.0%

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

   8. Simplified 61.0%

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

      1. associate-*l/ 55.4%

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

   10. Applied egg-rr 55.4%

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

   11. Taylor expanded in y around 0 50.1%

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

       1. *-commutative 50.1%

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

       2. times-frac 60.3%

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

   13. Simplified 60.3%

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

   if 2.39999999999999993e96 < b < 1.7e220

   1. Initial program 70.3%

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

      1. associate-*l* 70.3%

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

      2. associate-*l* 74.0%

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

   3. Simplified 74.0%

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

   4. Taylor expanded in x around inf 40.6%

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

      1. associate-*r/ 40.6%

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

      2. *-commutative 40.6%

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

      3. times-frac 47.9%

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

      4. associate-/l* 55.5%

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

   6. Simplified 55.5%

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

   if 1.7e220 < b

   1. Initial program 74.4%

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

      1. associate-*l* 74.4%

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

      2. associate-*l* 74.4%

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

   3. Simplified 74.4%

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

      1. *-un-lft-identity 74.4%

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

      2. *-commutative 74.4%

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

      3. times-frac 82.2%

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

   5. Applied egg-rr 82.2%

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

   6. Taylor expanded in b around inf 70.0%

      \[\leadsto \frac{1}{c} \cdot \color{blue}{\frac{b}{z}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+72}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{-302}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{-242}:\\ \;\;\;\;9 \cdot \frac{y \cdot \frac{x}{z}}{c}\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-77}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right)}{c}\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-7}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+96}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+220}:\\ \;\;\;\;\frac{9}{z} \cdot \frac{y}{\frac{c}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \end{array} \]

Alternative 6: 48.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{if}\;b \leq -1.1 \cdot 10^{+73}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{-239}:\\ \;\;\;\;9 \cdot \frac{y \cdot \frac{x}{z}}{c}\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-77}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right)}{c}\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-6}:\\ \;\;\;\;\frac{9 \cdot y}{z} \cdot \frac{x}{c}\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+220}:\\ \;\;\;\;\frac{9}{z} \cdot \frac{y}{\frac{c}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* t -4.0) (/ c a))))
   (if (<= b -1.1e+73)
     (/ (/ b c) z)
     (if (<= b -8.2e-302)
       t_1
       (if (<= b 1.06e-239)
         (* 9.0 (/ (* y (/ x z)) c))
         (if (<= b 2.9e-77)
           (/ (* a (* t -4.0)) c)
           (if (<= b 5.6e-6)
             (* (/ (* 9.0 y) z) (/ x c))
             (if (<= b 5.8e+96)
               t_1
               (if (<= b 1.7e+220)
                 (* (/ 9.0 z) (/ y (/ c x)))
                 (* (/ b z) (/ 1.0 c)))))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (t * -4.0) / (c / a);
	double tmp;
	if (b <= -1.1e+73) {
		tmp = (b / c) / z;
	} else if (b <= -8.2e-302) {
		tmp = t_1;
	} else if (b <= 1.06e-239) {
		tmp = 9.0 * ((y * (x / z)) / c);
	} else if (b <= 2.9e-77) {
		tmp = (a * (t * -4.0)) / c;
	} else if (b <= 5.6e-6) {
		tmp = ((9.0 * y) / z) * (x / c);
	} else if (b <= 5.8e+96) {
		tmp = t_1;
	} else if (b <= 1.7e+220) {
		tmp = (9.0 / z) * (y / (c / x));
	} else {
		tmp = (b / z) * (1.0 / c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * (-4.0d0)) / (c / a)
    if (b <= (-1.1d+73)) then
        tmp = (b / c) / z
    else if (b <= (-8.2d-302)) then
        tmp = t_1
    else if (b <= 1.06d-239) then
        tmp = 9.0d0 * ((y * (x / z)) / c)
    else if (b <= 2.9d-77) then
        tmp = (a * (t * (-4.0d0))) / c
    else if (b <= 5.6d-6) then
        tmp = ((9.0d0 * y) / z) * (x / c)
    else if (b <= 5.8d+96) then
        tmp = t_1
    else if (b <= 1.7d+220) then
        tmp = (9.0d0 / z) * (y / (c / x))
    else
        tmp = (b / z) * (1.0d0 / c)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (t * -4.0) / (c / a);
	double tmp;
	if (b <= -1.1e+73) {
		tmp = (b / c) / z;
	} else if (b <= -8.2e-302) {
		tmp = t_1;
	} else if (b <= 1.06e-239) {
		tmp = 9.0 * ((y * (x / z)) / c);
	} else if (b <= 2.9e-77) {
		tmp = (a * (t * -4.0)) / c;
	} else if (b <= 5.6e-6) {
		tmp = ((9.0 * y) / z) * (x / c);
	} else if (b <= 5.8e+96) {
		tmp = t_1;
	} else if (b <= 1.7e+220) {
		tmp = (9.0 / z) * (y / (c / x));
	} else {
		tmp = (b / z) * (1.0 / c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (t * -4.0) / (c / a)
	tmp = 0
	if b <= -1.1e+73:
		tmp = (b / c) / z
	elif b <= -8.2e-302:
		tmp = t_1
	elif b <= 1.06e-239:
		tmp = 9.0 * ((y * (x / z)) / c)
	elif b <= 2.9e-77:
		tmp = (a * (t * -4.0)) / c
	elif b <= 5.6e-6:
		tmp = ((9.0 * y) / z) * (x / c)
	elif b <= 5.8e+96:
		tmp = t_1
	elif b <= 1.7e+220:
		tmp = (9.0 / z) * (y / (c / x))
	else:
		tmp = (b / z) * (1.0 / c)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(t * -4.0) / Float64(c / a))
	tmp = 0.0
	if (b <= -1.1e+73)
		tmp = Float64(Float64(b / c) / z);
	elseif (b <= -8.2e-302)
		tmp = t_1;
	elseif (b <= 1.06e-239)
		tmp = Float64(9.0 * Float64(Float64(y * Float64(x / z)) / c));
	elseif (b <= 2.9e-77)
		tmp = Float64(Float64(a * Float64(t * -4.0)) / c);
	elseif (b <= 5.6e-6)
		tmp = Float64(Float64(Float64(9.0 * y) / z) * Float64(x / c));
	elseif (b <= 5.8e+96)
		tmp = t_1;
	elseif (b <= 1.7e+220)
		tmp = Float64(Float64(9.0 / z) * Float64(y / Float64(c / x)));
	else
		tmp = Float64(Float64(b / z) * Float64(1.0 / c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (t * -4.0) / (c / a);
	tmp = 0.0;
	if (b <= -1.1e+73)
		tmp = (b / c) / z;
	elseif (b <= -8.2e-302)
		tmp = t_1;
	elseif (b <= 1.06e-239)
		tmp = 9.0 * ((y * (x / z)) / c);
	elseif (b <= 2.9e-77)
		tmp = (a * (t * -4.0)) / c;
	elseif (b <= 5.6e-6)
		tmp = ((9.0 * y) / z) * (x / c);
	elseif (b <= 5.8e+96)
		tmp = t_1;
	elseif (b <= 1.7e+220)
		tmp = (9.0 / z) * (y / (c / x));
	else
		tmp = (b / z) * (1.0 / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(t * -4.0), $MachinePrecision] / N[(c / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.1e+73], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, -8.2e-302], t$95$1, If[LessEqual[b, 1.06e-239], N[(9.0 * N[(N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.9e-77], N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[b, 5.6e-6], N[(N[(N[(9.0 * y), $MachinePrecision] / z), $MachinePrecision] * N[(x / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.8e+96], t$95$1, If[LessEqual[b, 1.7e+220], N[(N[(9.0 / z), $MachinePrecision] * N[(y / N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / z), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -1.1e73

   1. Initial program 81.0%

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

      1. associate-*l* 81.0%

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

      2. associate-*l* 79.0%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in b around inf 58.1%

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

      1. associate-/r* 64.3%

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

   6. Simplified 64.3%

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

   if -1.1e73 < b < -8.1999999999999996e-302 or 5.59999999999999975e-6 < b < 5.79999999999999955e96

   1. Initial program 74.8%

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

      1. associate-*l* 74.8%

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

      2. associate-*l* 78.0%

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

   3. Simplified 78.0%

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

      1. *-un-lft-identity 78.0%

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

      2. *-commutative 78.0%

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

      3. times-frac 80.4%

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

   5. Applied egg-rr 80.4%

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

   6. Taylor expanded in z around inf 56.5%

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

      1. associate-*r/ 55.5%

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

      2. *-commutative 55.5%

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

      3. associate-*r* 55.5%

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

      4. *-commutative 55.5%

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

      5. associate-/l* 60.3%

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

   8. Simplified 60.3%

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

   if -8.1999999999999996e-302 < b < 1.06e-239

   1. Initial program 59.8%

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

      1. associate-/r* 67.4%

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

   3. Simplified 67.6%

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

      1. fma-udef 67.6%

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

   5. Applied egg-rr 67.6%

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

   6. Taylor expanded in x around inf 51.1%

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

      1. times-frac 75.5%

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

   8. Simplified 75.5%

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

      1. associate-*l/ 75.3%

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

   10. Applied egg-rr 75.3%

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

   if 1.06e-239 < b < 2.8999999999999999e-77

   1. Initial program 84.6%

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

      1. associate-/r* 87.5%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in z around inf 79.0%

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

      1. *-commutative 79.0%

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

      2. *-commutative 79.0%

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

      3. *-commutative 79.0%

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

      4. associate-*l* 79.0%

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

   6. Simplified 79.0%

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

   if 2.8999999999999999e-77 < b < 5.59999999999999975e-6

   1. Initial program 77.4%

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

      1. associate-/r* 77.4%

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

   3. Simplified 88.8%

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

      1. div-inv 88.8%

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

   5. Applied egg-rr 88.8%

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

   6. Taylor expanded in x around inf 50.1%

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

      1. associate-*r/ 50.1%

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

      2. associate-*r* 50.1%

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

      3. *-commutative 50.1%

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

      4. times-frac 60.4%

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

   8. Simplified 60.4%

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

   if 5.79999999999999955e96 < b < 1.7e220

   1. Initial program 70.3%

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

      1. associate-*l* 70.3%

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

      2. associate-*l* 74.0%

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

   3. Simplified 74.0%

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

   4. Taylor expanded in x around inf 40.6%

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

      1. associate-*r/ 40.6%

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

      2. *-commutative 40.6%

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

      3. times-frac 47.9%

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

      4. associate-/l* 55.5%

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

   6. Simplified 55.5%

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

   if 1.7e220 < b

   1. Initial program 74.4%

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

      1. associate-*l* 74.4%

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

      2. associate-*l* 74.4%

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

   3. Simplified 74.4%

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

      1. *-un-lft-identity 74.4%

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

      2. *-commutative 74.4%

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

      3. times-frac 82.2%

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

   5. Applied egg-rr 82.2%

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

   6. Taylor expanded in b around inf 70.0%

      \[\leadsto \frac{1}{c} \cdot \color{blue}{\frac{b}{z}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+73}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-302}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{-239}:\\ \;\;\;\;9 \cdot \frac{y \cdot \frac{x}{z}}{c}\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-77}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right)}{c}\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-6}:\\ \;\;\;\;\frac{9 \cdot y}{z} \cdot \frac{x}{c}\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+96}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+220}:\\ \;\;\;\;\frac{9}{z} \cdot \frac{y}{\frac{c}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \end{array} \]

Alternative 7: 48.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{if}\;b \leq -1 \cdot 10^{+73}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -6.1 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{-242}:\\ \;\;\;\;9 \cdot \frac{y \cdot \frac{x}{z}}{c}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-77}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right)}{c}\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{-6}:\\ \;\;\;\;\frac{y \cdot \frac{9}{z}}{\frac{c}{x}}\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+220}:\\ \;\;\;\;\frac{9}{z} \cdot \frac{y}{\frac{c}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* t -4.0) (/ c a))))
   (if (<= b -1e+73)
     (/ (/ b c) z)
     (if (<= b -6.1e-302)
       t_1
       (if (<= b 9.6e-242)
         (* 9.0 (/ (* y (/ x z)) c))
         (if (<= b 5.2e-77)
           (/ (* a (* t -4.0)) c)
           (if (<= b 6.4e-6)
             (/ (* y (/ 9.0 z)) (/ c x))
             (if (<= b 1.8e+97)
               t_1
               (if (<= b 1.7e+220)
                 (* (/ 9.0 z) (/ y (/ c x)))
                 (* (/ b z) (/ 1.0 c)))))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (t * -4.0) / (c / a);
	double tmp;
	if (b <= -1e+73) {
		tmp = (b / c) / z;
	} else if (b <= -6.1e-302) {
		tmp = t_1;
	} else if (b <= 9.6e-242) {
		tmp = 9.0 * ((y * (x / z)) / c);
	} else if (b <= 5.2e-77) {
		tmp = (a * (t * -4.0)) / c;
	} else if (b <= 6.4e-6) {
		tmp = (y * (9.0 / z)) / (c / x);
	} else if (b <= 1.8e+97) {
		tmp = t_1;
	} else if (b <= 1.7e+220) {
		tmp = (9.0 / z) * (y / (c / x));
	} else {
		tmp = (b / z) * (1.0 / c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * (-4.0d0)) / (c / a)
    if (b <= (-1d+73)) then
        tmp = (b / c) / z
    else if (b <= (-6.1d-302)) then
        tmp = t_1
    else if (b <= 9.6d-242) then
        tmp = 9.0d0 * ((y * (x / z)) / c)
    else if (b <= 5.2d-77) then
        tmp = (a * (t * (-4.0d0))) / c
    else if (b <= 6.4d-6) then
        tmp = (y * (9.0d0 / z)) / (c / x)
    else if (b <= 1.8d+97) then
        tmp = t_1
    else if (b <= 1.7d+220) then
        tmp = (9.0d0 / z) * (y / (c / x))
    else
        tmp = (b / z) * (1.0d0 / c)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (t * -4.0) / (c / a);
	double tmp;
	if (b <= -1e+73) {
		tmp = (b / c) / z;
	} else if (b <= -6.1e-302) {
		tmp = t_1;
	} else if (b <= 9.6e-242) {
		tmp = 9.0 * ((y * (x / z)) / c);
	} else if (b <= 5.2e-77) {
		tmp = (a * (t * -4.0)) / c;
	} else if (b <= 6.4e-6) {
		tmp = (y * (9.0 / z)) / (c / x);
	} else if (b <= 1.8e+97) {
		tmp = t_1;
	} else if (b <= 1.7e+220) {
		tmp = (9.0 / z) * (y / (c / x));
	} else {
		tmp = (b / z) * (1.0 / c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (t * -4.0) / (c / a)
	tmp = 0
	if b <= -1e+73:
		tmp = (b / c) / z
	elif b <= -6.1e-302:
		tmp = t_1
	elif b <= 9.6e-242:
		tmp = 9.0 * ((y * (x / z)) / c)
	elif b <= 5.2e-77:
		tmp = (a * (t * -4.0)) / c
	elif b <= 6.4e-6:
		tmp = (y * (9.0 / z)) / (c / x)
	elif b <= 1.8e+97:
		tmp = t_1
	elif b <= 1.7e+220:
		tmp = (9.0 / z) * (y / (c / x))
	else:
		tmp = (b / z) * (1.0 / c)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(t * -4.0) / Float64(c / a))
	tmp = 0.0
	if (b <= -1e+73)
		tmp = Float64(Float64(b / c) / z);
	elseif (b <= -6.1e-302)
		tmp = t_1;
	elseif (b <= 9.6e-242)
		tmp = Float64(9.0 * Float64(Float64(y * Float64(x / z)) / c));
	elseif (b <= 5.2e-77)
		tmp = Float64(Float64(a * Float64(t * -4.0)) / c);
	elseif (b <= 6.4e-6)
		tmp = Float64(Float64(y * Float64(9.0 / z)) / Float64(c / x));
	elseif (b <= 1.8e+97)
		tmp = t_1;
	elseif (b <= 1.7e+220)
		tmp = Float64(Float64(9.0 / z) * Float64(y / Float64(c / x)));
	else
		tmp = Float64(Float64(b / z) * Float64(1.0 / c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (t * -4.0) / (c / a);
	tmp = 0.0;
	if (b <= -1e+73)
		tmp = (b / c) / z;
	elseif (b <= -6.1e-302)
		tmp = t_1;
	elseif (b <= 9.6e-242)
		tmp = 9.0 * ((y * (x / z)) / c);
	elseif (b <= 5.2e-77)
		tmp = (a * (t * -4.0)) / c;
	elseif (b <= 6.4e-6)
		tmp = (y * (9.0 / z)) / (c / x);
	elseif (b <= 1.8e+97)
		tmp = t_1;
	elseif (b <= 1.7e+220)
		tmp = (9.0 / z) * (y / (c / x));
	else
		tmp = (b / z) * (1.0 / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(t * -4.0), $MachinePrecision] / N[(c / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1e+73], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[b, -6.1e-302], t$95$1, If[LessEqual[b, 9.6e-242], N[(9.0 * N[(N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.2e-77], N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[b, 6.4e-6], N[(N[(y * N[(9.0 / z), $MachinePrecision]), $MachinePrecision] / N[(c / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.8e+97], t$95$1, If[LessEqual[b, 1.7e+220], N[(N[(9.0 / z), $MachinePrecision] * N[(y / N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / z), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -9.99999999999999983e72

   1. Initial program 81.0%

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

      1. associate-*l* 81.0%

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

      2. associate-*l* 79.0%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in b around inf 58.1%

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

      1. associate-/r* 64.3%

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

   6. Simplified 64.3%

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

   if -9.99999999999999983e72 < b < -6.0999999999999997e-302 or 6.3999999999999997e-6 < b < 1.79999999999999983e97

   1. Initial program 74.8%

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

      1. associate-*l* 74.8%

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

      2. associate-*l* 78.0%

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

   3. Simplified 78.0%

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

      1. *-un-lft-identity 78.0%

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

      2. *-commutative 78.0%

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

      3. times-frac 80.4%

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

   5. Applied egg-rr 80.4%

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

   6. Taylor expanded in z around inf 56.5%

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

      1. associate-*r/ 55.5%

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

      2. *-commutative 55.5%

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

      3. associate-*r* 55.5%

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

      4. *-commutative 55.5%

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

      5. associate-/l* 60.3%

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

   8. Simplified 60.3%

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

   if -6.0999999999999997e-302 < b < 9.6000000000000004e-242

   1. Initial program 59.8%

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

      1. associate-/r* 67.4%

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

   3. Simplified 67.6%

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

      1. fma-udef 67.6%

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

   5. Applied egg-rr 67.6%

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

   6. Taylor expanded in x around inf 51.1%

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

      1. times-frac 75.5%

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

   8. Simplified 75.5%

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

      1. associate-*l/ 75.3%

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

   10. Applied egg-rr 75.3%

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

   if 9.6000000000000004e-242 < b < 5.2000000000000002e-77

   1. Initial program 84.6%

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

      1. associate-/r* 87.5%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in z around inf 79.0%

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

      1. *-commutative 79.0%

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

      2. *-commutative 79.0%

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

      3. *-commutative 79.0%

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

      4. associate-*l* 79.0%

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

   6. Simplified 79.0%

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

   if 5.2000000000000002e-77 < b < 6.3999999999999997e-6

   1. Initial program 77.4%

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

      1. associate-*l* 77.4%

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

      2. associate-*l* 83.1%

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

   3. Simplified 83.1%

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

   4. Taylor expanded in x around inf 50.1%

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

      1. associate-*r/ 50.1%

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

      2. *-commutative 50.1%

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

      3. times-frac 60.6%

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

      4. associate-/l* 60.5%

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

   6. Simplified 60.5%

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

      1. associate-*l/ 60.3%

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

   8. Applied egg-rr 60.3%

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

   if 1.79999999999999983e97 < b < 1.7e220

   1. Initial program 70.3%

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

      1. associate-*l* 70.3%

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

      2. associate-*l* 74.0%

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

   3. Simplified 74.0%

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

   4. Taylor expanded in x around inf 40.6%

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

      1. associate-*r/ 40.6%

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

      2. *-commutative 40.6%

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

      3. times-frac 47.9%

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

      4. associate-/l* 55.5%

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

   6. Simplified 55.5%

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

   if 1.7e220 < b

   1. Initial program 74.4%

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

      1. associate-*l* 74.4%

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

      2. associate-*l* 74.4%

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

   3. Simplified 74.4%

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

      1. *-un-lft-identity 74.4%

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

      2. *-commutative 74.4%

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

      3. times-frac 82.2%

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

   5. Applied egg-rr 82.2%

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

   6. Taylor expanded in b around inf 70.0%

      \[\leadsto \frac{1}{c} \cdot \color{blue}{\frac{b}{z}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+73}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -6.1 \cdot 10^{-302}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{-242}:\\ \;\;\;\;9 \cdot \frac{y \cdot \frac{x}{z}}{c}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-77}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right)}{c}\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{-6}:\\ \;\;\;\;\frac{y \cdot \frac{9}{z}}{\frac{c}{x}}\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+97}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+220}:\\ \;\;\;\;\frac{9}{z} \cdot \frac{y}{\frac{c}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \end{array} \]

Alternative 8: 89.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := x \cdot \left(9 \cdot y\right)\\ \mathbf{if}\;z \leq -5 \cdot 10^{-12} \lor \neg \left(z \leq 2.3 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b + t_1}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - t_1\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* x (* 9.0 y))))
   (if (or (<= z -5e-12) (not (<= z 2.3e-45)))
     (/ (+ (* t (* a -4.0)) (/ (+ b t_1) z)) c)
     (/ (- b (- (* (* z 4.0) (* t a)) t_1)) (* z c)))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x * (9.0 * y);
	double tmp;
	if ((z <= -5e-12) || !(z <= 2.3e-45)) {
		tmp = ((t * (a * -4.0)) + ((b + t_1) / z)) / c;
	} else {
		tmp = (b - (((z * 4.0) * (t * a)) - t_1)) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (9.0d0 * y)
    if ((z <= (-5d-12)) .or. (.not. (z <= 2.3d-45))) then
        tmp = ((t * (a * (-4.0d0))) + ((b + t_1) / z)) / c
    else
        tmp = (b - (((z * 4.0d0) * (t * a)) - t_1)) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x * (9.0 * y);
	double tmp;
	if ((z <= -5e-12) || !(z <= 2.3e-45)) {
		tmp = ((t * (a * -4.0)) + ((b + t_1) / z)) / c;
	} else {
		tmp = (b - (((z * 4.0) * (t * a)) - t_1)) / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = x * (9.0 * y)
	tmp = 0
	if (z <= -5e-12) or not (z <= 2.3e-45):
		tmp = ((t * (a * -4.0)) + ((b + t_1) / z)) / c
	else:
		tmp = (b - (((z * 4.0) * (t * a)) - t_1)) / (z * c)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(x * Float64(9.0 * y))
	tmp = 0.0
	if ((z <= -5e-12) || !(z <= 2.3e-45))
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(Float64(b + t_1) / z)) / c);
	else
		tmp = Float64(Float64(b - Float64(Float64(Float64(z * 4.0) * Float64(t * a)) - t_1)) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x * (9.0 * y);
	tmp = 0.0;
	if ((z <= -5e-12) || ~((z <= 2.3e-45)))
		tmp = ((t * (a * -4.0)) + ((b + t_1) / z)) / c;
	else
		tmp = (b - (((z * 4.0) * (t * a)) - t_1)) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -5e-12], N[Not[LessEqual[z, 2.3e-45]], $MachinePrecision]], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(N[(b + t$95$1), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b - N[(N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9999999999999997e-12 or 2.29999999999999992e-45 < z

   1. Initial program 62.0%

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

      1. associate-/r* 73.6%

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

   3. Simplified 89.0%

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

      1. fma-udef 89.0%

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

   5. Applied egg-rr 89.0%

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

   if -4.9999999999999997e-12 < z < 2.29999999999999992e-45

   1. Initial program 98.8%

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

      1. associate-*l* 98.8%

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

      2. associate-*l* 95.0%

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

   3. Simplified 95.0%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-12} \lor \neg \left(z \leq 2.3 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b + x \cdot \left(9 \cdot y\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \left(\left(z \cdot 4\right) \cdot \left(t \cdot a\right) - x \cdot \left(9 \cdot y\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 9: 91.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-12} \lor \neg \left(z \leq 3.9 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b + x \cdot \left(9 \cdot y\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
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 -5e-12) (not (<= z 3.9e-45)))
   (/ (+ (* t (* a -4.0)) (/ (+ b (* x (* 9.0 y))) z)) c)
   (/ (+ b (- (* y (* x 9.0)) (* a (* t (* z 4.0))))) (* z c))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -5e-12) || !(z <= 3.9e-45)) {
		tmp = ((t * (a * -4.0)) + ((b + (x * (9.0 * y))) / z)) / c;
	} else {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-5d-12)) .or. (.not. (z <= 3.9d-45))) then
        tmp = ((t * (a * (-4.0d0))) + ((b + (x * (9.0d0 * y))) / z)) / c
    else
        tmp = (b + ((y * (x * 9.0d0)) - (a * (t * (z * 4.0d0))))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -5e-12) || !(z <= 3.9e-45)) {
		tmp = ((t * (a * -4.0)) + ((b + (x * (9.0 * y))) / z)) / c;
	} else {
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -5e-12) or not (z <= 3.9e-45):
		tmp = ((t * (a * -4.0)) + ((b + (x * (9.0 * y))) / z)) / c
	else:
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -5e-12) || !(z <= 3.9e-45))
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(Float64(b + Float64(x * Float64(9.0 * y))) / z)) / c);
	else
		tmp = Float64(Float64(b + Float64(Float64(y * Float64(x * 9.0)) - Float64(a * Float64(t * Float64(z * 4.0))))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -5e-12) || ~((z <= 3.9e-45)))
		tmp = ((t * (a * -4.0)) + ((b + (x * (9.0 * y))) / z)) / c;
	else
		tmp = (b + ((y * (x * 9.0)) - (a * (t * (z * 4.0))))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
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, -5e-12], N[Not[LessEqual[z, 3.9e-45]], $MachinePrecision]], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(b + N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9999999999999997e-12 or 3.9e-45 < z

   1. Initial program 62.0%

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

      1. associate-/r* 73.6%

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

   3. Simplified 89.0%

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

      1. fma-udef 89.0%

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

   5. Applied egg-rr 89.0%

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

   if -4.9999999999999997e-12 < z < 3.9e-45

   1. Initial program 98.8%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-12} \lor \neg \left(z \leq 3.9 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b + x \cdot \left(9 \cdot y\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 10: 86.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-46} \lor \neg \left(z \leq 1.46 \cdot 10^{-192}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b + x \cdot \left(9 \cdot y\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= z -2e-46) (not (<= z 1.46e-192)))
   (/ (+ (* t (* a -4.0)) (/ (+ b (* x (* 9.0 y))) z)) c)
   (/ (+ b (* 9.0 (* x y))) (* z c))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2e-46) || !(z <= 1.46e-192)) {
		tmp = ((t * (a * -4.0)) + ((b + (x * (9.0 * y))) / z)) / c;
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((z <= (-2d-46)) .or. (.not. (z <= 1.46d-192))) then
        tmp = ((t * (a * (-4.0d0))) + ((b + (x * (9.0d0 * y))) / z)) / c
    else
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((z <= -2e-46) || !(z <= 1.46e-192)) {
		tmp = ((t * (a * -4.0)) + ((b + (x * (9.0 * y))) / z)) / c;
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (z <= -2e-46) or not (z <= 1.46e-192):
		tmp = ((t * (a * -4.0)) + ((b + (x * (9.0 * y))) / z)) / c
	else:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((z <= -2e-46) || !(z <= 1.46e-192))
		tmp = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(Float64(b + Float64(x * Float64(9.0 * y))) / z)) / c);
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((z <= -2e-46) || ~((z <= 1.46e-192)))
		tmp = ((t * (a * -4.0)) + ((b + (x * (9.0 * y))) / z)) / c;
	else
		tmp = (b + (9.0 * (x * y))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[z, -2e-46], N[Not[LessEqual[z, 1.46e-192]], $MachinePrecision]], N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $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 < -2.00000000000000005e-46 or 1.46000000000000002e-192 < z

   1. Initial program 68.2%

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

      1. associate-/r* 77.3%

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

   3. Simplified 89.9%

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

      1. fma-udef 89.9%

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

   5. Applied egg-rr 89.9%

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

   if -2.00000000000000005e-46 < z < 1.46000000000000002e-192

   1. Initial program 99.8%

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

      1. associate-*l* 99.7%

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

      2. associate-*l* 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in x around inf 89.1%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-46} \lor \neg \left(z \leq 1.46 \cdot 10^{-192}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b + x \cdot \left(9 \cdot y\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 11: 49.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{if}\;b \leq -6.2 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -7.3 \cdot 10^{-302}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-238}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+96}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right)}{c}\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+200}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (/ b c) z)) (t_2 (* 9.0 (* (/ y c) (/ x z)))))
   (if (<= b -6.2e+72)
     t_1
     (if (<= b -7.3e-302)
       (/ (* t -4.0) (/ c a))
       (if (<= b 3.1e-238)
         t_2
         (if (<= b 2.6e+96)
           (/ (* a (* t -4.0)) c)
           (if (<= b 2.6e+200) t_2 t_1)))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double t_2 = 9.0 * ((y / c) * (x / z));
	double tmp;
	if (b <= -6.2e+72) {
		tmp = t_1;
	} else if (b <= -7.3e-302) {
		tmp = (t * -4.0) / (c / a);
	} else if (b <= 3.1e-238) {
		tmp = t_2;
	} else if (b <= 2.6e+96) {
		tmp = (a * (t * -4.0)) / c;
	} else if (b <= 2.6e+200) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b / c) / z
    t_2 = 9.0d0 * ((y / c) * (x / z))
    if (b <= (-6.2d+72)) then
        tmp = t_1
    else if (b <= (-7.3d-302)) then
        tmp = (t * (-4.0d0)) / (c / a)
    else if (b <= 3.1d-238) then
        tmp = t_2
    else if (b <= 2.6d+96) then
        tmp = (a * (t * (-4.0d0))) / c
    else if (b <= 2.6d+200) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b / c) / z;
	double t_2 = 9.0 * ((y / c) * (x / z));
	double tmp;
	if (b <= -6.2e+72) {
		tmp = t_1;
	} else if (b <= -7.3e-302) {
		tmp = (t * -4.0) / (c / a);
	} else if (b <= 3.1e-238) {
		tmp = t_2;
	} else if (b <= 2.6e+96) {
		tmp = (a * (t * -4.0)) / c;
	} else if (b <= 2.6e+200) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (b / c) / z
	t_2 = 9.0 * ((y / c) * (x / z))
	tmp = 0
	if b <= -6.2e+72:
		tmp = t_1
	elif b <= -7.3e-302:
		tmp = (t * -4.0) / (c / a)
	elif b <= 3.1e-238:
		tmp = t_2
	elif b <= 2.6e+96:
		tmp = (a * (t * -4.0)) / c
	elif b <= 2.6e+200:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b / c) / z)
	t_2 = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)))
	tmp = 0.0
	if (b <= -6.2e+72)
		tmp = t_1;
	elseif (b <= -7.3e-302)
		tmp = Float64(Float64(t * -4.0) / Float64(c / a));
	elseif (b <= 3.1e-238)
		tmp = t_2;
	elseif (b <= 2.6e+96)
		tmp = Float64(Float64(a * Float64(t * -4.0)) / c);
	elseif (b <= 2.6e+200)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b / c) / z;
	t_2 = 9.0 * ((y / c) * (x / z));
	tmp = 0.0;
	if (b <= -6.2e+72)
		tmp = t_1;
	elseif (b <= -7.3e-302)
		tmp = (t * -4.0) / (c / a);
	elseif (b <= 3.1e-238)
		tmp = t_2;
	elseif (b <= 2.6e+96)
		tmp = (a * (t * -4.0)) / c;
	elseif (b <= 2.6e+200)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.2e+72], t$95$1, If[LessEqual[b, -7.3e-302], N[(N[(t * -4.0), $MachinePrecision] / N[(c / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.1e-238], t$95$2, If[LessEqual[b, 2.6e+96], N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[b, 2.6e+200], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.19999999999999977e72 or 2.6000000000000001e200 < b

   1. Initial program 77.9%

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

      1. associate-*l* 77.9%

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

      2. associate-*l* 76.7%

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

   3. Simplified 76.7%

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

   4. Taylor expanded in b around inf 56.9%

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

      1. associate-/r* 65.9%

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

   6. Simplified 65.9%

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

   if -6.19999999999999977e72 < b < -7.30000000000000009e-302

   1. Initial program 79.6%

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

      1. associate-*l* 79.6%

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

      2. associate-*l* 81.1%

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

   3. Simplified 81.1%

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

      1. *-un-lft-identity 81.1%

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

      2. *-commutative 81.1%

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

      3. times-frac 83.9%

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

   5. Applied egg-rr 83.9%

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

   6. Taylor expanded in z around inf 57.7%

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

      1. associate-*r/ 57.7%

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

      2. *-commutative 57.7%

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

      3. associate-*r* 57.7%

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

      4. *-commutative 57.7%

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

      5. associate-/l* 62.5%

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

   8. Simplified 62.5%

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

   if -7.30000000000000009e-302 < b < 3.1000000000000001e-238 or 2.6e96 < b < 2.6000000000000001e200

   1. Initial program 67.8%

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

      1. associate-/r* 75.6%

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

   3. Simplified 81.2%

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

      1. fma-udef 81.2%

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

   5. Applied egg-rr 81.2%

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

   6. Taylor expanded in x around inf 46.2%

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

      1. times-frac 65.2%

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

   8. Simplified 65.2%

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

   if 3.1000000000000001e-238 < b < 2.6e96

   1. Initial program 74.6%

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

      1. associate-/r* 74.8%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in z around inf 60.6%

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

      1. *-commutative 60.6%

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

      2. *-commutative 60.6%

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

      3. *-commutative 60.6%

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

      4. associate-*l* 60.6%

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

   6. Simplified 60.6%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+72}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq -7.3 \cdot 10^{-302}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-238}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+96}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right)}{c}\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+200}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 12: 74.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+113}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+30} \lor \neg \left(z \leq 10^{-114}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (* t (* a -4.0)) (/ b z)) c)))
   (if (<= z -1.65e+134)
     t_1
     (if (<= z -2.1e+113)
       (* 9.0 (* (/ y c) (/ x z)))
       (if (or (<= z -1.55e+30) (not (<= z 1e-114)))
         t_1
         (/ (+ b (* 9.0 (* x y))) (* z c)))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (z <= -1.65e+134) {
		tmp = t_1;
	} else if (z <= -2.1e+113) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else if ((z <= -1.55e+30) || !(z <= 1e-114)) {
		tmp = t_1;
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t * (a * (-4.0d0))) + (b / z)) / c
    if (z <= (-1.65d+134)) then
        tmp = t_1
    else if (z <= (-2.1d+113)) then
        tmp = 9.0d0 * ((y / c) * (x / z))
    else if ((z <= (-1.55d+30)) .or. (.not. (z <= 1d-114))) then
        tmp = t_1
    else
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (z <= -1.65e+134) {
		tmp = t_1;
	} else if (z <= -2.1e+113) {
		tmp = 9.0 * ((y / c) * (x / z));
	} else if ((z <= -1.55e+30) || !(z <= 1e-114)) {
		tmp = t_1;
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = ((t * (a * -4.0)) + (b / z)) / c
	tmp = 0
	if z <= -1.65e+134:
		tmp = t_1
	elif z <= -2.1e+113:
		tmp = 9.0 * ((y / c) * (x / z))
	elif (z <= -1.55e+30) or not (z <= 1e-114):
		tmp = t_1
	else:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -1.65e+134)
		tmp = t_1;
	elseif (z <= -2.1e+113)
		tmp = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)));
	elseif ((z <= -1.55e+30) || !(z <= 1e-114))
		tmp = t_1;
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	tmp = 0.0;
	if (z <= -1.65e+134)
		tmp = t_1;
	elseif (z <= -2.1e+113)
		tmp = 9.0 * ((y / c) * (x / z));
	elseif ((z <= -1.55e+30) || ~((z <= 1e-114)))
		tmp = t_1;
	else
		tmp = (b + (9.0 * (x * y))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.65e+134], t$95$1, If[LessEqual[z, -2.1e+113], N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.55e+30], N[Not[LessEqual[z, 1e-114]], $MachinePrecision]], t$95$1, N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.65e134 or -2.0999999999999999e113 < z < -1.5499999999999999e30 or 1.0000000000000001e-114 < z

   1. Initial program 63.5%

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

      1. associate-/r* 74.3%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in x around 0 77.5%

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

      1. *-commutative 77.5%

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

      2. *-commutative 77.5%

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

      3. associate-*l* 76.9%

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

   6. Simplified 76.9%

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

   if -1.65e134 < z < -2.0999999999999999e113

   1. Initial program 45.7%

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

      1. associate-/r* 59.3%

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

   3. Simplified 73.1%

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

      1. fma-udef 73.1%

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

   5. Applied egg-rr 73.1%

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

   6. Taylor expanded in x around inf 45.8%

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

      1. times-frac 85.7%

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

   8. Simplified 85.7%

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

   if -1.5499999999999999e30 < z < 1.0000000000000001e-114

   1. Initial program 97.8%

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

      1. associate-*l* 97.8%

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

      2. associate-*l* 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in x around inf 84.9%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+134}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+113}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+30} \lor \neg \left(z \leq 10^{-114}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 13: 74.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+91}:\\ \;\;\;\;\frac{\frac{b - y \cdot \left(x \cdot -9\right)}{z}}{c}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+33} \lor \neg \left(z \leq 5.9 \cdot 10^{-114}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (* t (* a -4.0)) (/ b z)) c)))
   (if (<= z -1.65e+134)
     t_1
     (if (<= z -1.9e+91)
       (/ (/ (- b (* y (* x -9.0))) z) c)
       (if (or (<= z -1.2e+33) (not (<= z 5.9e-114)))
         t_1
         (/ (+ b (* 9.0 (* x y))) (* z c)))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (z <= -1.65e+134) {
		tmp = t_1;
	} else if (z <= -1.9e+91) {
		tmp = ((b - (y * (x * -9.0))) / z) / c;
	} else if ((z <= -1.2e+33) || !(z <= 5.9e-114)) {
		tmp = t_1;
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t * (a * (-4.0d0))) + (b / z)) / c
    if (z <= (-1.65d+134)) then
        tmp = t_1
    else if (z <= (-1.9d+91)) then
        tmp = ((b - (y * (x * (-9.0d0)))) / z) / c
    else if ((z <= (-1.2d+33)) .or. (.not. (z <= 5.9d-114))) then
        tmp = t_1
    else
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (z <= -1.65e+134) {
		tmp = t_1;
	} else if (z <= -1.9e+91) {
		tmp = ((b - (y * (x * -9.0))) / z) / c;
	} else if ((z <= -1.2e+33) || !(z <= 5.9e-114)) {
		tmp = t_1;
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = ((t * (a * -4.0)) + (b / z)) / c
	tmp = 0
	if z <= -1.65e+134:
		tmp = t_1
	elif z <= -1.9e+91:
		tmp = ((b - (y * (x * -9.0))) / z) / c
	elif (z <= -1.2e+33) or not (z <= 5.9e-114):
		tmp = t_1
	else:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -1.65e+134)
		tmp = t_1;
	elseif (z <= -1.9e+91)
		tmp = Float64(Float64(Float64(b - Float64(y * Float64(x * -9.0))) / z) / c);
	elseif ((z <= -1.2e+33) || !(z <= 5.9e-114))
		tmp = t_1;
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	tmp = 0.0;
	if (z <= -1.65e+134)
		tmp = t_1;
	elseif (z <= -1.9e+91)
		tmp = ((b - (y * (x * -9.0))) / z) / c;
	elseif ((z <= -1.2e+33) || ~((z <= 5.9e-114)))
		tmp = t_1;
	else
		tmp = (b + (9.0 * (x * y))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.65e+134], t$95$1, If[LessEqual[z, -1.9e+91], N[(N[(N[(b - N[(y * N[(x * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / c), $MachinePrecision], If[Or[LessEqual[z, -1.2e+33], N[Not[LessEqual[z, 5.9e-114]], $MachinePrecision]], t$95$1, N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.65e134 or -1.8999999999999999e91 < z < -1.2e33 or 5.9000000000000001e-114 < z

   1. Initial program 62.6%

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

      1. associate-/r* 73.2%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in x around 0 77.2%

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

      1. *-commutative 77.2%

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

      2. *-commutative 77.2%

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

      3. associate-*l* 76.6%

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

   6. Simplified 76.6%

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

   if -1.65e134 < z < -1.8999999999999999e91

   1. Initial program 63.4%

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

      1. associate-/r* 78.1%

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

   3. Simplified 85.5%

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

   4. Taylor expanded in t around 0 85.6%

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

   5. Taylor expanded in z around -inf 85.5%

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

      1. associate-*r/ 85.5%

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

      2. mul-1-neg 85.5%

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

      3. mul-1-neg 85.5%

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

      4. unsub-neg 85.5%

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

      5. *-commutative 85.5%

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

      6. associate-*l* 85.5%

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

   7. Simplified 85.5%

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

   if -1.2e33 < z < 5.9000000000000001e-114

   1. Initial program 97.8%

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

      1. associate-*l* 97.8%

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

      2. associate-*l* 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in x around inf 84.9%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+134}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+91}:\\ \;\;\;\;\frac{\frac{b - y \cdot \left(x \cdot -9\right)}{z}}{c}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+33} \lor \neg \left(z \leq 5.9 \cdot 10^{-114}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 14: 73.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ t_2 := b + 9 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+91}:\\ \;\;\;\;\frac{1}{c} \cdot \frac{t_2}{z}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+33} \lor \neg \left(z \leq 2 \cdot 10^{-120}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (* t (* a -4.0)) (/ b z)) c)) (t_2 (+ b (* 9.0 (* x y)))))
   (if (<= z -1.65e+134)
     t_1
     (if (<= z -4e+91)
       (* (/ 1.0 c) (/ t_2 z))
       (if (or (<= z -2.5e+33) (not (<= z 2e-120))) t_1 (/ t_2 (* z c)))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	double t_2 = b + (9.0 * (x * y));
	double tmp;
	if (z <= -1.65e+134) {
		tmp = t_1;
	} else if (z <= -4e+91) {
		tmp = (1.0 / c) * (t_2 / z);
	} else if ((z <= -2.5e+33) || !(z <= 2e-120)) {
		tmp = t_1;
	} else {
		tmp = t_2 / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((t * (a * (-4.0d0))) + (b / z)) / c
    t_2 = b + (9.0d0 * (x * y))
    if (z <= (-1.65d+134)) then
        tmp = t_1
    else if (z <= (-4d+91)) then
        tmp = (1.0d0 / c) * (t_2 / z)
    else if ((z <= (-2.5d+33)) .or. (.not. (z <= 2d-120))) then
        tmp = t_1
    else
        tmp = t_2 / (z * c)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	double t_2 = b + (9.0 * (x * y));
	double tmp;
	if (z <= -1.65e+134) {
		tmp = t_1;
	} else if (z <= -4e+91) {
		tmp = (1.0 / c) * (t_2 / z);
	} else if ((z <= -2.5e+33) || !(z <= 2e-120)) {
		tmp = t_1;
	} else {
		tmp = t_2 / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = ((t * (a * -4.0)) + (b / z)) / c
	t_2 = b + (9.0 * (x * y))
	tmp = 0
	if z <= -1.65e+134:
		tmp = t_1
	elif z <= -4e+91:
		tmp = (1.0 / c) * (t_2 / z)
	elif (z <= -2.5e+33) or not (z <= 2e-120):
		tmp = t_1
	else:
		tmp = t_2 / (z * c)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c)
	t_2 = Float64(b + Float64(9.0 * Float64(x * y)))
	tmp = 0.0
	if (z <= -1.65e+134)
		tmp = t_1;
	elseif (z <= -4e+91)
		tmp = Float64(Float64(1.0 / c) * Float64(t_2 / z));
	elseif ((z <= -2.5e+33) || !(z <= 2e-120))
		tmp = t_1;
	else
		tmp = Float64(t_2 / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	t_2 = b + (9.0 * (x * y));
	tmp = 0.0;
	if (z <= -1.65e+134)
		tmp = t_1;
	elseif (z <= -4e+91)
		tmp = (1.0 / c) * (t_2 / z);
	elseif ((z <= -2.5e+33) || ~((z <= 2e-120)))
		tmp = t_1;
	else
		tmp = t_2 / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, Block[{t$95$2 = N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e+134], t$95$1, If[LessEqual[z, -4e+91], N[(N[(1.0 / c), $MachinePrecision] * N[(t$95$2 / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2.5e+33], N[Not[LessEqual[z, 2e-120]], $MachinePrecision]], t$95$1, N[(t$95$2 / N[(z * c), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.65e134 or -4.00000000000000032e91 < z < -2.49999999999999986e33 or 1.99999999999999996e-120 < z

   1. Initial program 62.6%

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

      1. associate-/r* 73.2%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in x around 0 77.2%

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

      1. *-commutative 77.2%

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

      2. *-commutative 77.2%

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

      3. associate-*l* 76.6%

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

   6. Simplified 76.6%

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

   if -1.65e134 < z < -4.00000000000000032e91

   1. Initial program 63.4%

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

      1. associate-*l* 63.5%

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

      2. associate-*l* 70.8%

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

   3. Simplified 70.8%

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

      1. *-un-lft-identity 70.8%

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

      2. *-commutative 70.8%

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

      3. times-frac 85.6%

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

   5. Applied egg-rr 85.6%

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

   6. Taylor expanded in z around 0 85.6%

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

   if -2.49999999999999986e33 < z < 1.99999999999999996e-120

   1. Initial program 97.8%

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

      1. associate-*l* 97.8%

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

      2. associate-*l* 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in x around inf 84.9%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+134}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+91}:\\ \;\;\;\;\frac{1}{c} \cdot \frac{b + 9 \cdot \left(x \cdot y\right)}{z}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+33} \lor \neg \left(z \leq 2 \cdot 10^{-120}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 15: 73.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+87}:\\ \;\;\;\;\frac{\frac{b}{z} + 9 \cdot \frac{x}{\frac{z}{y}}}{c}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+33} \lor \neg \left(z \leq 5.7 \cdot 10^{-118}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (* t (* a -4.0)) (/ b z)) c)))
   (if (<= z -1.65e+134)
     t_1
     (if (<= z -2.2e+87)
       (/ (+ (/ b z) (* 9.0 (/ x (/ z y)))) c)
       (if (or (<= z -3.6e+33) (not (<= z 5.7e-118)))
         t_1
         (/ (+ b (* 9.0 (* x y))) (* z c)))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (z <= -1.65e+134) {
		tmp = t_1;
	} else if (z <= -2.2e+87) {
		tmp = ((b / z) + (9.0 * (x / (z / y)))) / c;
	} else if ((z <= -3.6e+33) || !(z <= 5.7e-118)) {
		tmp = t_1;
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((t * (a * (-4.0d0))) + (b / z)) / c
    if (z <= (-1.65d+134)) then
        tmp = t_1
    else if (z <= (-2.2d+87)) then
        tmp = ((b / z) + (9.0d0 * (x / (z / y)))) / c
    else if ((z <= (-3.6d+33)) .or. (.not. (z <= 5.7d-118))) then
        tmp = t_1
    else
        tmp = (b + (9.0d0 * (x * y))) / (z * c)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	double tmp;
	if (z <= -1.65e+134) {
		tmp = t_1;
	} else if (z <= -2.2e+87) {
		tmp = ((b / z) + (9.0 * (x / (z / y)))) / c;
	} else if ((z <= -3.6e+33) || !(z <= 5.7e-118)) {
		tmp = t_1;
	} else {
		tmp = (b + (9.0 * (x * y))) / (z * c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = ((t * (a * -4.0)) + (b / z)) / c
	tmp = 0
	if z <= -1.65e+134:
		tmp = t_1
	elif z <= -2.2e+87:
		tmp = ((b / z) + (9.0 * (x / (z / y)))) / c
	elif (z <= -3.6e+33) or not (z <= 5.7e-118):
		tmp = t_1
	else:
		tmp = (b + (9.0 * (x * y))) / (z * c)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(t * Float64(a * -4.0)) + Float64(b / z)) / c)
	tmp = 0.0
	if (z <= -1.65e+134)
		tmp = t_1;
	elseif (z <= -2.2e+87)
		tmp = Float64(Float64(Float64(b / z) + Float64(9.0 * Float64(x / Float64(z / y)))) / c);
	elseif ((z <= -3.6e+33) || !(z <= 5.7e-118))
		tmp = t_1;
	else
		tmp = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((t * (a * -4.0)) + (b / z)) / c;
	tmp = 0.0;
	if (z <= -1.65e+134)
		tmp = t_1;
	elseif (z <= -2.2e+87)
		tmp = ((b / z) + (9.0 * (x / (z / y)))) / c;
	elseif ((z <= -3.6e+33) || ~((z <= 5.7e-118)))
		tmp = t_1;
	else
		tmp = (b + (9.0 * (x * y))) / (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[z, -1.65e+134], t$95$1, If[LessEqual[z, -2.2e+87], N[(N[(N[(b / z), $MachinePrecision] + N[(9.0 * N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[Or[LessEqual[z, -3.6e+33], N[Not[LessEqual[z, 5.7e-118]], $MachinePrecision]], t$95$1, N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.65e134 or -2.2000000000000001e87 < z < -3.6000000000000003e33 or 5.70000000000000012e-118 < z

   1. Initial program 62.6%

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

      1. associate-/r* 73.2%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in x around 0 77.2%

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

      1. *-commutative 77.2%

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

      2. *-commutative 77.2%

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

      3. associate-*l* 76.6%

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

   6. Simplified 76.6%

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

   if -1.65e134 < z < -2.2000000000000001e87

   1. Initial program 63.4%

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

      1. associate-/r* 78.1%

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

   3. Simplified 85.5%

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

      1. fma-udef 85.5%

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

   5. Applied egg-rr 85.5%

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

   6. Taylor expanded in t around 0 85.6%

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

      1. *-commutative 85.6%

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

      2. associate-/l* 99.8%

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

   8. Simplified 99.8%

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

   if -3.6000000000000003e33 < z < 5.70000000000000012e-118

   1. Initial program 97.8%

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

      1. associate-*l* 97.8%

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

      2. associate-*l* 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in x around inf 84.9%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+134}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+87}:\\ \;\;\;\;\frac{\frac{b}{z} + 9 \cdot \frac{x}{\frac{z}{y}}}{c}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+33} \lor \neg \left(z \leq 5.7 \cdot 10^{-118}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 16: 65.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+134}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+41}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ b (* 9.0 (* x y))) (* z c))))
   (if (<= z -3.5e+134)
     (/ (* a (* t -4.0)) c)
     (if (<= z -6.2e+88)
       t_1
       (if (<= z -6.5e+41)
         (* -4.0 (/ a (/ c t)))
         (if (<= z 2.5e-45) t_1 (/ (* t -4.0) (/ c a))))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + (9.0 * (x * y))) / (z * c);
	double tmp;
	if (z <= -3.5e+134) {
		tmp = (a * (t * -4.0)) / c;
	} else if (z <= -6.2e+88) {
		tmp = t_1;
	} else if (z <= -6.5e+41) {
		tmp = -4.0 * (a / (c / t));
	} else if (z <= 2.5e-45) {
		tmp = t_1;
	} else {
		tmp = (t * -4.0) / (c / a);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b + (9.0d0 * (x * y))) / (z * c)
    if (z <= (-3.5d+134)) then
        tmp = (a * (t * (-4.0d0))) / c
    else if (z <= (-6.2d+88)) then
        tmp = t_1
    else if (z <= (-6.5d+41)) then
        tmp = (-4.0d0) * (a / (c / t))
    else if (z <= 2.5d-45) then
        tmp = t_1
    else
        tmp = (t * (-4.0d0)) / (c / a)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + (9.0 * (x * y))) / (z * c);
	double tmp;
	if (z <= -3.5e+134) {
		tmp = (a * (t * -4.0)) / c;
	} else if (z <= -6.2e+88) {
		tmp = t_1;
	} else if (z <= -6.5e+41) {
		tmp = -4.0 * (a / (c / t));
	} else if (z <= 2.5e-45) {
		tmp = t_1;
	} else {
		tmp = (t * -4.0) / (c / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = (b + (9.0 * (x * y))) / (z * c)
	tmp = 0
	if z <= -3.5e+134:
		tmp = (a * (t * -4.0)) / c
	elif z <= -6.2e+88:
		tmp = t_1
	elif z <= -6.5e+41:
		tmp = -4.0 * (a / (c / t))
	elif z <= 2.5e-45:
		tmp = t_1
	else:
		tmp = (t * -4.0) / (c / a)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b + Float64(9.0 * Float64(x * y))) / Float64(z * c))
	tmp = 0.0
	if (z <= -3.5e+134)
		tmp = Float64(Float64(a * Float64(t * -4.0)) / c);
	elseif (z <= -6.2e+88)
		tmp = t_1;
	elseif (z <= -6.5e+41)
		tmp = Float64(-4.0 * Float64(a / Float64(c / t)));
	elseif (z <= 2.5e-45)
		tmp = t_1;
	else
		tmp = Float64(Float64(t * -4.0) / Float64(c / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b + (9.0 * (x * y))) / (z * c);
	tmp = 0.0;
	if (z <= -3.5e+134)
		tmp = (a * (t * -4.0)) / c;
	elseif (z <= -6.2e+88)
		tmp = t_1;
	elseif (z <= -6.5e+41)
		tmp = -4.0 * (a / (c / t));
	elseif (z <= 2.5e-45)
		tmp = t_1;
	else
		tmp = (t * -4.0) / (c / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b + N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5e+134], N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, -6.2e+88], t$95$1, If[LessEqual[z, -6.5e+41], N[(-4.0 * N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e-45], t$95$1, N[(N[(t * -4.0), $MachinePrecision] / N[(c / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.50000000000000003e134

   1. Initial program 51.1%

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

      1. associate-/r* 68.2%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in z around inf 68.0%

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

      1. *-commutative 68.0%

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

      2. *-commutative 68.0%

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

      3. *-commutative 68.0%

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

      4. associate-*l* 68.0%

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

   6. Simplified 68.0%

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

   if -3.50000000000000003e134 < z < -6.2000000000000003e88 or -6.49999999999999975e41 < z < 2.49999999999999988e-45

   1. Initial program 94.6%

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

      1. associate-*l* 94.5%

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

      2. associate-*l* 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in x around inf 81.5%

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

   if -6.2000000000000003e88 < z < -6.49999999999999975e41

   1. Initial program 71.3%

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

      1. associate-*l* 71.3%

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

      2. associate-*l* 71.5%

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

   3. Simplified 71.5%

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

   4. Taylor expanded in z around inf 71.4%

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

      1. *-commutative 71.4%

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

      2. associate-/l* 71.2%

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

   6. Simplified 71.2%

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

   if 2.49999999999999988e-45 < z

   1. Initial program 59.8%

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

      1. associate-*l* 59.7%

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

      2. associate-*l* 69.6%

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

   3. Simplified 69.6%

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

      1. *-un-lft-identity 69.6%

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

      2. *-commutative 69.6%

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

      3. times-frac 81.6%

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

   5. Applied egg-rr 81.6%

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

   6. Taylor expanded in z around inf 63.1%

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

      1. associate-*r/ 63.1%

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

      2. *-commutative 63.1%

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

      3. associate-*r* 63.1%

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

      4. *-commutative 63.1%

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

      5. associate-/l* 66.3%

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

   8. Simplified 66.3%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+134}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+88}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+41}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-45}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \end{array} \]

Alternative 17: 71.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;b \leq -1100:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+197}:\\ \;\;\;\;\frac{t_1 + \frac{x \cdot y}{\frac{z}{9}}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0))))
   (if (<= b -1100.0)
     (/ (- b (* 4.0 (* a (* z t)))) (* z c))
     (if (<= b 5.2e+197)
       (/ (+ t_1 (/ (* x y) (/ z 9.0))) c)
       (/ (+ t_1 (/ b z)) c)))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (b <= -1100.0) {
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c);
	} else if (b <= 5.2e+197) {
		tmp = (t_1 + ((x * y) / (z / 9.0))) / c;
	} else {
		tmp = (t_1 + (b / z)) / c;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (a * (-4.0d0))
    if (b <= (-1100.0d0)) then
        tmp = (b - (4.0d0 * (a * (z * t)))) / (z * c)
    else if (b <= 5.2d+197) then
        tmp = (t_1 + ((x * y) / (z / 9.0d0))) / c
    else
        tmp = (t_1 + (b / z)) / c
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = t * (a * -4.0);
	double tmp;
	if (b <= -1100.0) {
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c);
	} else if (b <= 5.2e+197) {
		tmp = (t_1 + ((x * y) / (z / 9.0))) / c;
	} else {
		tmp = (t_1 + (b / z)) / c;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	t_1 = t * (a * -4.0)
	tmp = 0
	if b <= -1100.0:
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c)
	elif b <= 5.2e+197:
		tmp = (t_1 + ((x * y) / (z / 9.0))) / c
	else:
		tmp = (t_1 + (b / z)) / c
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	t_1 = Float64(t * Float64(a * -4.0))
	tmp = 0.0
	if (b <= -1100.0)
		tmp = Float64(Float64(b - Float64(4.0 * Float64(a * Float64(z * t)))) / Float64(z * c));
	elseif (b <= 5.2e+197)
		tmp = Float64(Float64(t_1 + Float64(Float64(x * y) / Float64(z / 9.0))) / c);
	else
		tmp = Float64(Float64(t_1 + Float64(b / z)) / c);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = t * (a * -4.0);
	tmp = 0.0;
	if (b <= -1100.0)
		tmp = (b - (4.0 * (a * (z * t)))) / (z * c);
	elseif (b <= 5.2e+197)
		tmp = (t_1 + ((x * y) / (z / 9.0))) / c;
	else
		tmp = (t_1 + (b / z)) / c;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1100.0], N[(N[(b - N[(4.0 * N[(a * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.2e+197], N[(N[(t$95$1 + N[(N[(x * y), $MachinePrecision] / N[(z / 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(t$95$1 + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1100

   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%

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

      2. associate-*l* 79.2%

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

   3. Simplified 79.2%

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

   4. Taylor expanded in x around 0 74.5%

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

   if -1100 < b < 5.19999999999999975e197

   1. Initial program 73.9%

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

      1. associate-/r* 76.3%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in x around inf 79.5%

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

      1. associate-*r/ 79.6%

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

      2. *-commutative 79.6%

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

      3. associate-/l* 79.6%

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

   6. Simplified 79.6%

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

   if 5.19999999999999975e197 < b

   1. Initial program 72.9%

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

      1. associate-/r* 83.3%

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

   3. Simplified 86.8%

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

   4. Taylor expanded in x around 0 82.9%

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

      1. *-commutative 82.9%

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

      2. *-commutative 82.9%

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

      3. associate-*l* 82.9%

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

   6. Simplified 82.9%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1100:\\ \;\;\;\;\frac{b - 4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+197}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{x \cdot y}{\frac{z}{9}}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 18: 51.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+72} \lor \neg \left(b \leq 5.5 \cdot 10^{+92}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \frac{a}{c}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -5.2e+72) (not (<= b 5.5e+92)))
   (/ (/ b c) z)
   (* (* t -4.0) (/ a c))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -5.2e+72) || !(b <= 5.5e+92)) {
		tmp = (b / c) / z;
	} else {
		tmp = (t * -4.0) * (a / c);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-5.2d+72)) .or. (.not. (b <= 5.5d+92))) then
        tmp = (b / c) / z
    else
        tmp = (t * (-4.0d0)) * (a / c)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -5.2e+72) || !(b <= 5.5e+92)) {
		tmp = (b / c) / z;
	} else {
		tmp = (t * -4.0) * (a / c);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -5.2e+72) or not (b <= 5.5e+92):
		tmp = (b / c) / z
	else:
		tmp = (t * -4.0) * (a / c)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -5.2e+72) || !(b <= 5.5e+92))
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(Float64(t * -4.0) * Float64(a / c));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -5.2e+72) || ~((b <= 5.5e+92)))
		tmp = (b / c) / z;
	else
		tmp = (t * -4.0) * (a / c);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -5.2e+72], N[Not[LessEqual[b, 5.5e+92]], $MachinePrecision]], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(t * -4.0), $MachinePrecision] * N[(a / c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.19999999999999963e72 or 5.50000000000000053e92 < b

   1. Initial program 76.7%

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

      1. associate-*l* 76.7%

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

      2. associate-*l* 76.7%

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

   3. Simplified 76.7%

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

   4. Taylor expanded in b around inf 51.2%

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

      1. associate-/r* 58.8%

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

   6. Simplified 58.8%

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

   if -5.19999999999999963e72 < b < 5.50000000000000053e92

   1. Initial program 75.8%

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

      1. associate-/r* 75.5%

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

   3. Simplified 86.6%

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

      1. fma-udef 86.6%

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

   5. Applied egg-rr 86.6%

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

   6. Taylor expanded in z around inf 55.8%

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

      1. *-commutative 55.8%

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

      2. associate-/l* 56.3%

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

      3. associate-/r/ 56.4%

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

      4. associate-*r* 56.4%

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

      5. *-commutative 56.4%

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

      6. *-commutative 56.4%

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

   8. Simplified 56.4%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+72} \lor \neg \left(b \leq 5.5 \cdot 10^{+92}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot -4\right) \cdot \frac{a}{c}\\ \end{array} \]

Alternative 19: 51.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+72} \lor \neg \left(b \leq 4 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -6e+72) (not (<= b 4e+85)))
   (/ (/ b c) z)
   (/ (* t -4.0) (/ c a))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -6e+72) || !(b <= 4e+85)) {
		tmp = (b / c) / z;
	} else {
		tmp = (t * -4.0) / (c / a);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-6d+72)) .or. (.not. (b <= 4d+85))) then
        tmp = (b / c) / z
    else
        tmp = (t * (-4.0d0)) / (c / a)
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -6e+72) || !(b <= 4e+85)) {
		tmp = (b / c) / z;
	} else {
		tmp = (t * -4.0) / (c / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -6e+72) or not (b <= 4e+85):
		tmp = (b / c) / z
	else:
		tmp = (t * -4.0) / (c / a)
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -6e+72) || !(b <= 4e+85))
		tmp = Float64(Float64(b / c) / z);
	else
		tmp = Float64(Float64(t * -4.0) / Float64(c / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -6e+72) || ~((b <= 4e+85)))
		tmp = (b / c) / z;
	else
		tmp = (t * -4.0) / (c / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -6e+72], N[Not[LessEqual[b, 4e+85]], $MachinePrecision]], N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision], N[(N[(t * -4.0), $MachinePrecision] / N[(c / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.00000000000000006e72 or 4.0000000000000001e85 < b

   1. Initial program 76.7%

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

      1. associate-*l* 76.7%

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

      2. associate-*l* 76.7%

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

   3. Simplified 76.7%

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

   4. Taylor expanded in b around inf 51.2%

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

      1. associate-/r* 58.8%

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

   6. Simplified 58.8%

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

   if -6.00000000000000006e72 < b < 4.0000000000000001e85

   1. Initial program 75.8%

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

      1. associate-*l* 75.7%

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

      2. associate-*l* 79.5%

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

   3. Simplified 79.5%

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

      1. *-un-lft-identity 79.5%

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

      2. *-commutative 79.5%

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

      3. times-frac 82.2%

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

   5. Applied egg-rr 82.2%

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

   6. Taylor expanded in z around inf 55.8%

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

      1. associate-*r/ 55.2%

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

      2. *-commutative 55.2%

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

      3. associate-*r* 55.2%

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

      4. *-commutative 55.2%

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

      5. associate-/l* 57.0%

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

   8. Simplified 57.0%

      \[\leadsto \color{blue}{\frac{t \cdot -4}{\frac{c}{a}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+72} \lor \neg \left(b \leq 4 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \end{array} \]

Alternative 20: 35.2% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.1%

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

   1. associate-*l* 76.1%

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

   2. associate-*l* 78.4%

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

3. Simplified 78.4%

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

4. Taylor expanded in b around inf 32.2%

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

   1. *-commutative 32.2%

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

6. Simplified 32.2%

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

7. Final simplification 32.2%

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

Alternative 21: 35.2% accurate, 3.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 76.1%

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

   1. associate-*l* 76.1%

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

   2. associate-*l* 78.4%

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

3. Simplified 78.4%

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

4. Taylor expanded in b around inf 32.2%

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

   1. associate-/r* 35.2%

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

6. Simplified 35.2%

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

7. Final simplification 35.2%

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

Developer target: 79.7% 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 2023185 
(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)))