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

Percentage Accurate: 91.6% → 96.7%

Time: 10.6s

Alternatives: 14

Speedup: 0.6×

• 28.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = ((x * y) - ((z * 9.0d0) * t)) / (a * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

Python

def code(x, y, z, t, a):
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 91.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = ((x * y) - ((z * 9.0d0) * t)) / (a * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
}

Python

def code(x, y, z, t, a):
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 96.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+233}:\\ \;\;\;\;\mathsf{fma}\left(-4.5, z \cdot \frac{t}{a}, 0.5 \cdot \left(x \cdot \frac{y}{a}\right)\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+273}:\\ \;\;\;\;\frac{t_1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4.5, t \cdot \frac{z}{a}, \frac{x}{a} \cdot \left(y \cdot 0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_1 -5e+233)
     (fma -4.5 (* z (/ t a)) (* 0.5 (* x (/ y a))))
     (if (<= t_1 2e+273)
       (/ t_1 (* a 2.0))
       (fma -4.5 (* t (/ z a)) (* (/ x a) (* y 0.5)))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -5e+233) {
		tmp = fma(-4.5, (z * (t / a)), (0.5 * (x * (y / a))));
	} else if (t_1 <= 2e+273) {
		tmp = t_1 / (a * 2.0);
	} else {
		tmp = fma(-4.5, (t * (z / a)), ((x / a) * (y * 0.5)));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_1 <= -5e+233)
		tmp = fma(-4.5, Float64(z * Float64(t / a)), Float64(0.5 * Float64(x * Float64(y / a))));
	elseif (t_1 <= 2e+273)
		tmp = Float64(t_1 / Float64(a * 2.0));
	else
		tmp = fma(-4.5, Float64(t * Float64(z / a)), Float64(Float64(x / a) * Float64(y * 0.5)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+233], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+273], N[(t$95$1 / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision] + N[(N[(x / a), $MachinePrecision] * N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < -5.00000000000000009e233

   1. Initial program 73.3%

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

      1. associate-*l* 71.3%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 71.3%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 73.3%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. fma-def 73.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4.5, \frac{t \cdot z}{a}, 0.5 \cdot \frac{x \cdot y}{a}\right)} \]

      2. associate-/l* 85.5%

         \[\leadsto \mathsf{fma}\left(-4.5, \color{blue}{\frac{t}{\frac{a}{z}}}, 0.5 \cdot \frac{x \cdot y}{a}\right) \]

      3. associate-/r/ 83.3%

         \[\leadsto \mathsf{fma}\left(-4.5, \color{blue}{\frac{t}{a} \cdot z}, 0.5 \cdot \frac{x \cdot y}{a}\right) \]

      4. associate-*r/ 95.4%

         \[\leadsto \mathsf{fma}\left(-4.5, \frac{t}{a} \cdot z, 0.5 \cdot \color{blue}{\left(x \cdot \frac{y}{a}\right)}\right) \]

   7. Simplified 95.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4.5, \frac{t}{a} \cdot z, 0.5 \cdot \left(x \cdot \frac{y}{a}\right)\right)} \]

   if -5.00000000000000009e233 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 1.99999999999999989e273

   1. Initial program 98.7%

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

   if 1.99999999999999989e273 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 59.4%

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

      1. associate-*l* 59.4%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 59.4%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 59.4%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y - 9 \cdot \left(t \cdot z\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 59.4%

         \[\leadsto \color{blue}{\frac{0.5 \cdot \left(x \cdot y - 9 \cdot \left(t \cdot z\right)\right)}{a}} \]

      2. cancel-sign-sub-inv 59.4%

         \[\leadsto \frac{0.5 \cdot \color{blue}{\left(x \cdot y + \left(-9\right) \cdot \left(t \cdot z\right)\right)}}{a} \]

      3. metadata-eval 59.4%

         \[\leadsto \frac{0.5 \cdot \left(x \cdot y + \color{blue}{-9} \cdot \left(t \cdot z\right)\right)}{a} \]

      4. +-commutative 59.4%

         \[\leadsto \frac{0.5 \cdot \color{blue}{\left(-9 \cdot \left(t \cdot z\right) + x \cdot y\right)}}{a} \]

      5. associate-/l* 59.4%

         \[\leadsto \color{blue}{\frac{0.5}{\frac{a}{-9 \cdot \left(t \cdot z\right) + x \cdot y}}} \]

      6. +-commutative 59.4%

         \[\leadsto \frac{0.5}{\frac{a}{\color{blue}{x \cdot y + -9 \cdot \left(t \cdot z\right)}}} \]

      7. metadata-eval 59.4%

         \[\leadsto \frac{0.5}{\frac{a}{x \cdot y + \color{blue}{\left(-9\right)} \cdot \left(t \cdot z\right)}} \]

      8. cancel-sign-sub-inv 59.4%

         \[\leadsto \frac{0.5}{\frac{a}{\color{blue}{x \cdot y - 9 \cdot \left(t \cdot z\right)}}} \]

      9. fma-neg 67.3%

         \[\leadsto \frac{0.5}{\frac{a}{\color{blue}{\mathsf{fma}\left(x, y, -9 \cdot \left(t \cdot z\right)\right)}}} \]

      10. *-commutative 67.3%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, -9 \cdot \color{blue}{\left(z \cdot t\right)}\right)}} \]

      11. distribute-lft-neg-in 67.3%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9\right) \cdot \left(z \cdot t\right)}\right)}} \]

      12. metadata-eval 67.3%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9} \cdot \left(z \cdot t\right)\right)}} \]

      13. *-commutative 67.3%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(z \cdot t\right) \cdot -9}\right)}} \]

      14. associate-*l* 67.3%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(t \cdot -9\right)}\right)}} \]

   7. Simplified 67.3%

      \[\leadsto \color{blue}{\frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   8. Taylor expanded in x around 0 59.4%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \frac{x \cdot y}{a}} \]
   9. Step-by-step derivation

      1. fma-def 59.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4.5, \frac{t \cdot z}{a}, 0.5 \cdot \frac{x \cdot y}{a}\right)} \]

      2. associate-*r/ 71.8%

         \[\leadsto \mathsf{fma}\left(-4.5, \color{blue}{t \cdot \frac{z}{a}}, 0.5 \cdot \frac{x \cdot y}{a}\right) \]

      3. associate-*l/ 86.8%

         \[\leadsto \mathsf{fma}\left(-4.5, t \cdot \frac{z}{a}, 0.5 \cdot \color{blue}{\left(\frac{x}{a} \cdot y\right)}\right) \]

      4. *-commutative 86.8%

         \[\leadsto \mathsf{fma}\left(-4.5, t \cdot \frac{z}{a}, 0.5 \cdot \color{blue}{\left(y \cdot \frac{x}{a}\right)}\right) \]

      5. *-commutative 86.8%

         \[\leadsto \mathsf{fma}\left(-4.5, t \cdot \frac{z}{a}, \color{blue}{\left(y \cdot \frac{x}{a}\right) \cdot 0.5}\right) \]

      6. *-commutative 86.8%

         \[\leadsto \mathsf{fma}\left(-4.5, t \cdot \frac{z}{a}, \color{blue}{\left(\frac{x}{a} \cdot y\right)} \cdot 0.5\right) \]

      7. associate-*r* 86.8%

         \[\leadsto \mathsf{fma}\left(-4.5, t \cdot \frac{z}{a}, \color{blue}{\frac{x}{a} \cdot \left(y \cdot 0.5\right)}\right) \]

   10. Simplified 86.8%

       \[\leadsto \color{blue}{\mathsf{fma}\left(-4.5, t \cdot \frac{z}{a}, \frac{x}{a} \cdot \left(y \cdot 0.5\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -5 \cdot 10^{+233}:\\ \;\;\;\;\mathsf{fma}\left(-4.5, z \cdot \frac{t}{a}, 0.5 \cdot \left(x \cdot \frac{y}{a}\right)\right)\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+273}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4.5, t \cdot \frac{z}{a}, \frac{x}{a} \cdot \left(y \cdot 0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 5 \cdot 10^{-115}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4.5, t \cdot \frac{z}{a}, \frac{x}{a} \cdot \left(y \cdot 0.5\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 2.0) 5e-115)
   (/ (fma x y (* z (* t -9.0))) (* a 2.0))
   (fma -4.5 (* t (/ z a)) (* (/ x a) (* y 0.5)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 2.0) <= 5e-115) {
		tmp = fma(x, y, (z * (t * -9.0))) / (a * 2.0);
	} else {
		tmp = fma(-4.5, (t * (z / a)), ((x / a) * (y * 0.5)));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 2.0) <= 5e-115)
		tmp = Float64(fma(x, y, Float64(z * Float64(t * -9.0))) / Float64(a * 2.0));
	else
		tmp = fma(-4.5, Float64(t * Float64(z / a)), Float64(Float64(x / a) * Float64(y * 0.5)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 2.0), $MachinePrecision], 5e-115], N[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision] + N[(N[(x / a), $MachinePrecision] * N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 2) < 5.0000000000000003e-115

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

         \[\leadsto \frac{\color{blue}{y \cdot x} - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

      2. *-commutative 90.6%

         \[\leadsto \frac{\color{blue}{x \cdot y} - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

      3. cancel-sign-sub-inv 90.6%

         \[\leadsto \frac{\color{blue}{x \cdot y + \left(-z \cdot 9\right) \cdot t}}{a \cdot 2} \]

      4. fma-def 91.8%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, y, \left(-z \cdot 9\right) \cdot t\right)}}{a \cdot 2} \]

      5. distribute-rgt-neg-in 91.8%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{\left(z \cdot \left(-9\right)\right)} \cdot t\right)}{a \cdot 2} \]

      6. associate-*r* 91.2%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(\left(-9\right) \cdot t\right)}\right)}{a \cdot 2} \]

      7. distribute-lft-neg-in 91.2%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(-9 \cdot t\right)}\right)}{a \cdot 2} \]

      8. *-commutative 91.2%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \left(-\color{blue}{t \cdot 9}\right)\right)}{a \cdot 2} \]

      9. distribute-rgt-neg-in 91.2%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(t \cdot \left(-9\right)\right)}\right)}{a \cdot 2} \]

      10. metadata-eval 91.2%

          \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot \color{blue}{-9}\right)\right)}{a \cdot 2} \]

   3. Simplified 91.2%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   if 5.0000000000000003e-115 < (*.f64 a 2)

   1. Initial program 84.2%

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

      1. associate-*l* 84.2%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 84.2%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 84.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y - 9 \cdot \left(t \cdot z\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 84.2%

         \[\leadsto \color{blue}{\frac{0.5 \cdot \left(x \cdot y - 9 \cdot \left(t \cdot z\right)\right)}{a}} \]

      2. cancel-sign-sub-inv 84.2%

         \[\leadsto \frac{0.5 \cdot \color{blue}{\left(x \cdot y + \left(-9\right) \cdot \left(t \cdot z\right)\right)}}{a} \]

      3. metadata-eval 84.2%

         \[\leadsto \frac{0.5 \cdot \left(x \cdot y + \color{blue}{-9} \cdot \left(t \cdot z\right)\right)}{a} \]

      4. +-commutative 84.2%

         \[\leadsto \frac{0.5 \cdot \color{blue}{\left(-9 \cdot \left(t \cdot z\right) + x \cdot y\right)}}{a} \]

      5. associate-/l* 84.2%

         \[\leadsto \color{blue}{\frac{0.5}{\frac{a}{-9 \cdot \left(t \cdot z\right) + x \cdot y}}} \]

      6. +-commutative 84.2%

         \[\leadsto \frac{0.5}{\frac{a}{\color{blue}{x \cdot y + -9 \cdot \left(t \cdot z\right)}}} \]

      7. metadata-eval 84.2%

         \[\leadsto \frac{0.5}{\frac{a}{x \cdot y + \color{blue}{\left(-9\right)} \cdot \left(t \cdot z\right)}} \]

      8. cancel-sign-sub-inv 84.2%

         \[\leadsto \frac{0.5}{\frac{a}{\color{blue}{x \cdot y - 9 \cdot \left(t \cdot z\right)}}} \]

      9. fma-neg 85.3%

         \[\leadsto \frac{0.5}{\frac{a}{\color{blue}{\mathsf{fma}\left(x, y, -9 \cdot \left(t \cdot z\right)\right)}}} \]

      10. *-commutative 85.3%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, -9 \cdot \color{blue}{\left(z \cdot t\right)}\right)}} \]

      11. distribute-lft-neg-in 85.3%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9\right) \cdot \left(z \cdot t\right)}\right)}} \]

      12. metadata-eval 85.3%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9} \cdot \left(z \cdot t\right)\right)}} \]

      13. *-commutative 85.3%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(z \cdot t\right) \cdot -9}\right)}} \]

      14. associate-*l* 85.2%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(t \cdot -9\right)}\right)}} \]

   7. Simplified 85.2%

      \[\leadsto \color{blue}{\frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   8. Taylor expanded in x around 0 84.3%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \frac{x \cdot y}{a}} \]
   9. Step-by-step derivation

      1. fma-def 84.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-4.5, \frac{t \cdot z}{a}, 0.5 \cdot \frac{x \cdot y}{a}\right)} \]

      2. associate-*r/ 83.7%

         \[\leadsto \mathsf{fma}\left(-4.5, \color{blue}{t \cdot \frac{z}{a}}, 0.5 \cdot \frac{x \cdot y}{a}\right) \]

      3. associate-*l/ 89.7%

         \[\leadsto \mathsf{fma}\left(-4.5, t \cdot \frac{z}{a}, 0.5 \cdot \color{blue}{\left(\frac{x}{a} \cdot y\right)}\right) \]

      4. *-commutative 89.7%

         \[\leadsto \mathsf{fma}\left(-4.5, t \cdot \frac{z}{a}, 0.5 \cdot \color{blue}{\left(y \cdot \frac{x}{a}\right)}\right) \]

      5. *-commutative 89.7%

         \[\leadsto \mathsf{fma}\left(-4.5, t \cdot \frac{z}{a}, \color{blue}{\left(y \cdot \frac{x}{a}\right) \cdot 0.5}\right) \]

      6. *-commutative 89.7%

         \[\leadsto \mathsf{fma}\left(-4.5, t \cdot \frac{z}{a}, \color{blue}{\left(\frac{x}{a} \cdot y\right)} \cdot 0.5\right) \]

      7. associate-*r* 89.7%

         \[\leadsto \mathsf{fma}\left(-4.5, t \cdot \frac{z}{a}, \color{blue}{\frac{x}{a} \cdot \left(y \cdot 0.5\right)}\right) \]

   10. Simplified 89.7%

       \[\leadsto \color{blue}{\mathsf{fma}\left(-4.5, t \cdot \frac{z}{a}, \frac{x}{a} \cdot \left(y \cdot 0.5\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 5 \cdot 10^{-115}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4.5, t \cdot \frac{z}{a}, \frac{x}{a} \cdot \left(y \cdot 0.5\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 10^{+91}:\\ \;\;\;\;\frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \frac{x}{2} - \left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{0.5}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 2.0) 1e+91)
   (/ 0.5 (/ a (fma x y (* z (* t -9.0)))))
   (- (* (/ y a) (/ x 2.0)) (* (* 9.0 (* z t)) (/ 0.5 a)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 2.0) <= 1e+91) {
		tmp = 0.5 / (a / fma(x, y, (z * (t * -9.0))));
	} else {
		tmp = ((y / a) * (x / 2.0)) - ((9.0 * (z * t)) * (0.5 / a));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 2.0) <= 1e+91)
		tmp = Float64(0.5 / Float64(a / fma(x, y, Float64(z * Float64(t * -9.0)))));
	else
		tmp = Float64(Float64(Float64(y / a) * Float64(x / 2.0)) - Float64(Float64(9.0 * Float64(z * t)) * Float64(0.5 / a)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 2.0), $MachinePrecision], 1e+91], N[(0.5 / N[(a / N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / a), $MachinePrecision] * N[(x / 2.0), $MachinePrecision]), $MachinePrecision] - N[(N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 2) < 1.00000000000000008e91

   1. Initial program 90.4%

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

      1. associate-*l* 89.9%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 89.9%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 90.4%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y - 9 \cdot \left(t \cdot z\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 90.4%

         \[\leadsto \color{blue}{\frac{0.5 \cdot \left(x \cdot y - 9 \cdot \left(t \cdot z\right)\right)}{a}} \]

      2. cancel-sign-sub-inv 90.4%

         \[\leadsto \frac{0.5 \cdot \color{blue}{\left(x \cdot y + \left(-9\right) \cdot \left(t \cdot z\right)\right)}}{a} \]

      3. metadata-eval 90.4%

         \[\leadsto \frac{0.5 \cdot \left(x \cdot y + \color{blue}{-9} \cdot \left(t \cdot z\right)\right)}{a} \]

      4. +-commutative 90.4%

         \[\leadsto \frac{0.5 \cdot \color{blue}{\left(-9 \cdot \left(t \cdot z\right) + x \cdot y\right)}}{a} \]

      5. associate-/l* 90.3%

         \[\leadsto \color{blue}{\frac{0.5}{\frac{a}{-9 \cdot \left(t \cdot z\right) + x \cdot y}}} \]

      6. +-commutative 90.3%

         \[\leadsto \frac{0.5}{\frac{a}{\color{blue}{x \cdot y + -9 \cdot \left(t \cdot z\right)}}} \]

      7. metadata-eval 90.3%

         \[\leadsto \frac{0.5}{\frac{a}{x \cdot y + \color{blue}{\left(-9\right)} \cdot \left(t \cdot z\right)}} \]

      8. cancel-sign-sub-inv 90.3%

         \[\leadsto \frac{0.5}{\frac{a}{\color{blue}{x \cdot y - 9 \cdot \left(t \cdot z\right)}}} \]

      9. fma-neg 91.7%

         \[\leadsto \frac{0.5}{\frac{a}{\color{blue}{\mathsf{fma}\left(x, y, -9 \cdot \left(t \cdot z\right)\right)}}} \]

      10. *-commutative 91.7%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, -9 \cdot \color{blue}{\left(z \cdot t\right)}\right)}} \]

      11. distribute-lft-neg-in 91.7%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9\right) \cdot \left(z \cdot t\right)}\right)}} \]

      12. metadata-eval 91.7%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9} \cdot \left(z \cdot t\right)\right)}} \]

      13. *-commutative 91.7%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(z \cdot t\right) \cdot -9}\right)}} \]

      14. associate-*l* 91.2%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(t \cdot -9\right)}\right)}} \]

   7. Simplified 91.2%

      \[\leadsto \color{blue}{\frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]

   if 1.00000000000000008e91 < (*.f64 a 2)

   1. Initial program 78.4%

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

      1. associate-*l* 78.4%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 78.4%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. div-sub 78.5%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a \cdot 2} - \frac{z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

      2. *-commutative 78.5%

         \[\leadsto \frac{x \cdot y}{\color{blue}{2 \cdot a}} - \frac{z \cdot \left(9 \cdot t\right)}{a \cdot 2} \]

      3. times-frac 89.1%

         \[\leadsto \color{blue}{\frac{x}{2} \cdot \frac{y}{a}} - \frac{z \cdot \left(9 \cdot t\right)}{a \cdot 2} \]

      4. div-inv 89.0%

         \[\leadsto \frac{x}{2} \cdot \frac{y}{a} - \color{blue}{\left(z \cdot \left(9 \cdot t\right)\right) \cdot \frac{1}{a \cdot 2}} \]

      5. associate-*r* 89.1%

         \[\leadsto \frac{x}{2} \cdot \frac{y}{a} - \color{blue}{\left(\left(z \cdot 9\right) \cdot t\right)} \cdot \frac{1}{a \cdot 2} \]

      6. *-commutative 89.1%

         \[\leadsto \frac{x}{2} \cdot \frac{y}{a} - \left(\color{blue}{\left(9 \cdot z\right)} \cdot t\right) \cdot \frac{1}{a \cdot 2} \]

      7. associate-*l* 89.0%

         \[\leadsto \frac{x}{2} \cdot \frac{y}{a} - \color{blue}{\left(9 \cdot \left(z \cdot t\right)\right)} \cdot \frac{1}{a \cdot 2} \]

      8. *-commutative 89.0%

         \[\leadsto \frac{x}{2} \cdot \frac{y}{a} - \left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{1}{\color{blue}{2 \cdot a}} \]

      9. associate-/r* 89.0%

         \[\leadsto \frac{x}{2} \cdot \frac{y}{a} - \left(9 \cdot \left(z \cdot t\right)\right) \cdot \color{blue}{\frac{\frac{1}{2}}{a}} \]

      10. metadata-eval 89.0%

          \[\leadsto \frac{x}{2} \cdot \frac{y}{a} - \left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{\color{blue}{0.5}}{a} \]

   6. Applied egg-rr 89.0%

      \[\leadsto \color{blue}{\frac{x}{2} \cdot \frac{y}{a} - \left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{0.5}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 10^{+91}:\\ \;\;\;\;\frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \frac{x}{2} - \left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 5 \cdot 10^{+77}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \frac{x}{2} - \left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{0.5}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 2.0) 5e+77)
   (/ (fma x y (* z (* t -9.0))) (* a 2.0))
   (- (* (/ y a) (/ x 2.0)) (* (* 9.0 (* z t)) (/ 0.5 a)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 2.0) <= 5e+77) {
		tmp = fma(x, y, (z * (t * -9.0))) / (a * 2.0);
	} else {
		tmp = ((y / a) * (x / 2.0)) - ((9.0 * (z * t)) * (0.5 / a));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 2.0) <= 5e+77)
		tmp = Float64(fma(x, y, Float64(z * Float64(t * -9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(Float64(y / a) * Float64(x / 2.0)) - Float64(Float64(9.0 * Float64(z * t)) * Float64(0.5 / a)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 2.0), $MachinePrecision], 5e+77], N[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / a), $MachinePrecision] * N[(x / 2.0), $MachinePrecision]), $MachinePrecision] - N[(N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 2) < 5.00000000000000004e77

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

         \[\leadsto \frac{\color{blue}{y \cdot x} - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

      2. *-commutative 90.6%

         \[\leadsto \frac{\color{blue}{x \cdot y} - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

      3. cancel-sign-sub-inv 90.6%

         \[\leadsto \frac{\color{blue}{x \cdot y + \left(-z \cdot 9\right) \cdot t}}{a \cdot 2} \]

      4. fma-def 92.1%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, y, \left(-z \cdot 9\right) \cdot t\right)}}{a \cdot 2} \]

      5. distribute-rgt-neg-in 92.1%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{\left(z \cdot \left(-9\right)\right)} \cdot t\right)}{a \cdot 2} \]

      6. associate-*r* 91.6%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(\left(-9\right) \cdot t\right)}\right)}{a \cdot 2} \]

      7. distribute-lft-neg-in 91.6%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(-9 \cdot t\right)}\right)}{a \cdot 2} \]

      8. *-commutative 91.6%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \left(-\color{blue}{t \cdot 9}\right)\right)}{a \cdot 2} \]

      9. distribute-rgt-neg-in 91.6%

         \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(t \cdot \left(-9\right)\right)}\right)}{a \cdot 2} \]

      10. metadata-eval 91.6%

          \[\leadsto \frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot \color{blue}{-9}\right)\right)}{a \cdot 2} \]

   3. Simplified 91.6%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   if 5.00000000000000004e77 < (*.f64 a 2)

   1. Initial program 78.3%

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

      1. associate-*l* 78.3%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 78.3%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. div-sub 78.3%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a \cdot 2} - \frac{z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]

      2. *-commutative 78.3%

         \[\leadsto \frac{x \cdot y}{\color{blue}{2 \cdot a}} - \frac{z \cdot \left(9 \cdot t\right)}{a \cdot 2} \]

      3. times-frac 89.4%

         \[\leadsto \color{blue}{\frac{x}{2} \cdot \frac{y}{a}} - \frac{z \cdot \left(9 \cdot t\right)}{a \cdot 2} \]

      4. div-inv 89.3%

         \[\leadsto \frac{x}{2} \cdot \frac{y}{a} - \color{blue}{\left(z \cdot \left(9 \cdot t\right)\right) \cdot \frac{1}{a \cdot 2}} \]

      5. associate-*r* 89.4%

         \[\leadsto \frac{x}{2} \cdot \frac{y}{a} - \color{blue}{\left(\left(z \cdot 9\right) \cdot t\right)} \cdot \frac{1}{a \cdot 2} \]

      6. *-commutative 89.4%

         \[\leadsto \frac{x}{2} \cdot \frac{y}{a} - \left(\color{blue}{\left(9 \cdot z\right)} \cdot t\right) \cdot \frac{1}{a \cdot 2} \]

      7. associate-*l* 89.3%

         \[\leadsto \frac{x}{2} \cdot \frac{y}{a} - \color{blue}{\left(9 \cdot \left(z \cdot t\right)\right)} \cdot \frac{1}{a \cdot 2} \]

      8. *-commutative 89.3%

         \[\leadsto \frac{x}{2} \cdot \frac{y}{a} - \left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{1}{\color{blue}{2 \cdot a}} \]

      9. associate-/r* 89.3%

         \[\leadsto \frac{x}{2} \cdot \frac{y}{a} - \left(9 \cdot \left(z \cdot t\right)\right) \cdot \color{blue}{\frac{\frac{1}{2}}{a}} \]

      10. metadata-eval 89.3%

          \[\leadsto \frac{x}{2} \cdot \frac{y}{a} - \left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{\color{blue}{0.5}}{a} \]

   6. Applied egg-rr 89.3%

      \[\leadsto \color{blue}{\frac{x}{2} \cdot \frac{y}{a} - \left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{0.5}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 5 \cdot 10^{+77}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \frac{x}{2} - \left(9 \cdot \left(z \cdot t\right)\right) \cdot \frac{0.5}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+107}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-8}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-38} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+62}\right):\\ \;\;\;\;\frac{y \cdot 0.5}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e+107)
   (* 0.5 (/ x (/ a y)))
   (if (<= (* x y) -2e-8)
     (* -4.5 (* z (/ t a)))
     (if (or (<= (* x y) -5e-38) (not (<= (* x y) 5e+62)))
       (/ (* y 0.5) (/ a x))
       (* -4.5 (/ (* z t) a))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+107) {
		tmp = 0.5 * (x / (a / y));
	} else if ((x * y) <= -2e-8) {
		tmp = -4.5 * (z * (t / a));
	} else if (((x * y) <= -5e-38) || !((x * y) <= 5e+62)) {
		tmp = (y * 0.5) / (a / x);
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((x * y) <= (-2d+107)) then
        tmp = 0.5d0 * (x / (a / y))
    else if ((x * y) <= (-2d-8)) then
        tmp = (-4.5d0) * (z * (t / a))
    else if (((x * y) <= (-5d-38)) .or. (.not. ((x * y) <= 5d+62))) then
        tmp = (y * 0.5d0) / (a / x)
    else
        tmp = (-4.5d0) * ((z * t) / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+107) {
		tmp = 0.5 * (x / (a / y));
	} else if ((x * y) <= -2e-8) {
		tmp = -4.5 * (z * (t / a));
	} else if (((x * y) <= -5e-38) || !((x * y) <= 5e+62)) {
		tmp = (y * 0.5) / (a / x);
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e+107:
		tmp = 0.5 * (x / (a / y))
	elif (x * y) <= -2e-8:
		tmp = -4.5 * (z * (t / a))
	elif ((x * y) <= -5e-38) or not ((x * y) <= 5e+62):
		tmp = (y * 0.5) / (a / x)
	else:
		tmp = -4.5 * ((z * t) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e+107)
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	elseif (Float64(x * y) <= -2e-8)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	elseif ((Float64(x * y) <= -5e-38) || !(Float64(x * y) <= 5e+62))
		tmp = Float64(Float64(y * 0.5) / Float64(a / x));
	else
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2e+107)
		tmp = 0.5 * (x / (a / y));
	elseif ((x * y) <= -2e-8)
		tmp = -4.5 * (z * (t / a));
	elseif (((x * y) <= -5e-38) || ~(((x * y) <= 5e+62)))
		tmp = (y * 0.5) / (a / x);
	else
		tmp = -4.5 * ((z * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+107], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e-8], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(x * y), $MachinePrecision], -5e-38], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e+62]], $MachinePrecision]], N[(N[(y * 0.5), $MachinePrecision] / N[(a / x), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.9999999999999999e107

   1. Initial program 75.9%

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

      1. associate-*l* 73.9%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 73.9%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 78.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 91.2%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} \]

   7. Simplified 91.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{\frac{a}{y}}} \]

   if -1.9999999999999999e107 < (*.f64 x y) < -2e-8

   1. Initial program 88.9%

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

      1. associate-*l* 88.9%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 54.4%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 65.3%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

   7. Simplified 65.3%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t}{\frac{a}{z}}} \]
   8. Step-by-step derivation

      1. associate-/r/ 59.7%

         \[\leadsto -4.5 \cdot \color{blue}{\left(\frac{t}{a} \cdot z\right)} \]

   9. Applied egg-rr 59.7%

      \[\leadsto -4.5 \cdot \color{blue}{\left(\frac{t}{a} \cdot z\right)} \]

   if -2e-8 < (*.f64 x y) < -5.00000000000000033e-38 or 5.00000000000000029e62 < (*.f64 x y)

   1. Initial program 78.7%

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

      1. associate-*l* 78.7%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 78.7%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 76.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 76.3%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} \]

   7. Simplified 76.3%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{\frac{a}{y}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 76.3%

         \[\leadsto \color{blue}{\frac{0.5 \cdot x}{\frac{a}{y}}} \]

      2. associate-/l* 76.2%

         \[\leadsto \color{blue}{\frac{0.5}{\frac{\frac{a}{y}}{x}}} \]

      3. associate-/l/ 76.5%

         \[\leadsto \frac{0.5}{\color{blue}{\frac{a}{x \cdot y}}} \]

      4. *-commutative 76.5%

         \[\leadsto \frac{0.5}{\frac{a}{\color{blue}{y \cdot x}}} \]

      5. associate-/l* 76.5%

         \[\leadsto \color{blue}{\frac{0.5 \cdot \left(y \cdot x\right)}{a}} \]

      6. associate-*l* 76.5%

         \[\leadsto \frac{\color{blue}{\left(0.5 \cdot y\right) \cdot x}}{a} \]

      7. associate-/l* 84.4%

         \[\leadsto \color{blue}{\frac{0.5 \cdot y}{\frac{a}{x}}} \]

      8. *-commutative 84.4%

         \[\leadsto \frac{\color{blue}{y \cdot 0.5}}{\frac{a}{x}} \]

   9. Applied egg-rr 84.4%

      \[\leadsto \color{blue}{\frac{y \cdot 0.5}{\frac{a}{x}}} \]

   if -5.00000000000000033e-38 < (*.f64 x y) < 5.00000000000000029e62

   1. Initial program 95.3%

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

      1. associate-*l* 95.3%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 95.3%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 77.0%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+107}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-8}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-38} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+62}\right):\\ \;\;\;\;\frac{y \cdot 0.5}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+107}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-8}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-38} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+62}\right):\\ \;\;\;\;\frac{y \cdot 0.5}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e+107)
   (* 0.5 (/ x (/ a y)))
   (if (<= (* x y) -2e-8)
     (* -4.5 (* z (/ t a)))
     (if (or (<= (* x y) -5e-38) (not (<= (* x y) 5e+62)))
       (/ (* y 0.5) (/ a x))
       (/ (* t (* z -4.5)) a)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+107) {
		tmp = 0.5 * (x / (a / y));
	} else if ((x * y) <= -2e-8) {
		tmp = -4.5 * (z * (t / a));
	} else if (((x * y) <= -5e-38) || !((x * y) <= 5e+62)) {
		tmp = (y * 0.5) / (a / x);
	} else {
		tmp = (t * (z * -4.5)) / a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((x * y) <= (-2d+107)) then
        tmp = 0.5d0 * (x / (a / y))
    else if ((x * y) <= (-2d-8)) then
        tmp = (-4.5d0) * (z * (t / a))
    else if (((x * y) <= (-5d-38)) .or. (.not. ((x * y) <= 5d+62))) then
        tmp = (y * 0.5d0) / (a / x)
    else
        tmp = (t * (z * (-4.5d0))) / a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+107) {
		tmp = 0.5 * (x / (a / y));
	} else if ((x * y) <= -2e-8) {
		tmp = -4.5 * (z * (t / a));
	} else if (((x * y) <= -5e-38) || !((x * y) <= 5e+62)) {
		tmp = (y * 0.5) / (a / x);
	} else {
		tmp = (t * (z * -4.5)) / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e+107:
		tmp = 0.5 * (x / (a / y))
	elif (x * y) <= -2e-8:
		tmp = -4.5 * (z * (t / a))
	elif ((x * y) <= -5e-38) or not ((x * y) <= 5e+62):
		tmp = (y * 0.5) / (a / x)
	else:
		tmp = (t * (z * -4.5)) / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e+107)
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	elseif (Float64(x * y) <= -2e-8)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	elseif ((Float64(x * y) <= -5e-38) || !(Float64(x * y) <= 5e+62))
		tmp = Float64(Float64(y * 0.5) / Float64(a / x));
	else
		tmp = Float64(Float64(t * Float64(z * -4.5)) / a);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2e+107)
		tmp = 0.5 * (x / (a / y));
	elseif ((x * y) <= -2e-8)
		tmp = -4.5 * (z * (t / a));
	elseif (((x * y) <= -5e-38) || ~(((x * y) <= 5e+62)))
		tmp = (y * 0.5) / (a / x);
	else
		tmp = (t * (z * -4.5)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+107], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e-8], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(x * y), $MachinePrecision], -5e-38], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e+62]], $MachinePrecision]], N[(N[(y * 0.5), $MachinePrecision] / N[(a / x), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(z * -4.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.9999999999999999e107

   1. Initial program 75.9%

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

      1. associate-*l* 73.9%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 73.9%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 78.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 91.2%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} \]

   7. Simplified 91.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{\frac{a}{y}}} \]

   if -1.9999999999999999e107 < (*.f64 x y) < -2e-8

   1. Initial program 88.9%

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

      1. associate-*l* 88.9%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 54.4%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 65.3%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

   7. Simplified 65.3%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t}{\frac{a}{z}}} \]
   8. Step-by-step derivation

      1. associate-/r/ 59.7%

         \[\leadsto -4.5 \cdot \color{blue}{\left(\frac{t}{a} \cdot z\right)} \]

   9. Applied egg-rr 59.7%

      \[\leadsto -4.5 \cdot \color{blue}{\left(\frac{t}{a} \cdot z\right)} \]

   if -2e-8 < (*.f64 x y) < -5.00000000000000033e-38 or 5.00000000000000029e62 < (*.f64 x y)

   1. Initial program 78.7%

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

      1. associate-*l* 78.7%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 78.7%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 76.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 76.3%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} \]

   7. Simplified 76.3%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{\frac{a}{y}}} \]
   8. Step-by-step derivation

      1. associate-*r/ 76.3%

         \[\leadsto \color{blue}{\frac{0.5 \cdot x}{\frac{a}{y}}} \]

      2. associate-/l* 76.2%

         \[\leadsto \color{blue}{\frac{0.5}{\frac{\frac{a}{y}}{x}}} \]

      3. associate-/l/ 76.5%

         \[\leadsto \frac{0.5}{\color{blue}{\frac{a}{x \cdot y}}} \]

      4. *-commutative 76.5%

         \[\leadsto \frac{0.5}{\frac{a}{\color{blue}{y \cdot x}}} \]

      5. associate-/l* 76.5%

         \[\leadsto \color{blue}{\frac{0.5 \cdot \left(y \cdot x\right)}{a}} \]

      6. associate-*l* 76.5%

         \[\leadsto \frac{\color{blue}{\left(0.5 \cdot y\right) \cdot x}}{a} \]

      7. associate-/l* 84.4%

         \[\leadsto \color{blue}{\frac{0.5 \cdot y}{\frac{a}{x}}} \]

      8. *-commutative 84.4%

         \[\leadsto \frac{\color{blue}{y \cdot 0.5}}{\frac{a}{x}} \]

   9. Applied egg-rr 84.4%

      \[\leadsto \color{blue}{\frac{y \cdot 0.5}{\frac{a}{x}}} \]

   if -5.00000000000000033e-38 < (*.f64 x y) < 5.00000000000000029e62

   1. Initial program 95.3%

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

      1. associate-*l* 95.3%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 95.3%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 77.0%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 77.1%

         \[\leadsto \color{blue}{\frac{-4.5 \cdot \left(t \cdot z\right)}{a}} \]

      2. *-commutative 77.1%

         \[\leadsto \frac{-4.5 \cdot \color{blue}{\left(z \cdot t\right)}}{a} \]

      3. associate-*r* 77.1%

         \[\leadsto \frac{\color{blue}{\left(-4.5 \cdot z\right) \cdot t}}{a} \]

   7. Simplified 77.1%

      \[\leadsto \color{blue}{\frac{\left(-4.5 \cdot z\right) \cdot t}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+107}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-8}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-38} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+62}\right):\\ \;\;\;\;\frac{y \cdot 0.5}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := 0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-8}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-25}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+21}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 0.5 (/ x (/ a y)))))
   (if (<= (* x y) -2e+107)
     t_1
     (if (<= (* x y) -2e-8)
       (* -4.5 (* z (/ t a)))
       (if (<= (* x y) -2e-25)
         (* (* x y) (/ 0.5 a))
         (if (<= (* x y) 4e+21) (* -4.5 (/ (* z t) a)) t_1))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (x / (a / y));
	double tmp;
	if ((x * y) <= -2e+107) {
		tmp = t_1;
	} else if ((x * y) <= -2e-8) {
		tmp = -4.5 * (z * (t / a));
	} else if ((x * y) <= -2e-25) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 4e+21) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    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) :: t_1
    real(8) :: tmp
    t_1 = 0.5d0 * (x / (a / y))
    if ((x * y) <= (-2d+107)) then
        tmp = t_1
    else if ((x * y) <= (-2d-8)) then
        tmp = (-4.5d0) * (z * (t / a))
    else if ((x * y) <= (-2d-25)) then
        tmp = (x * y) * (0.5d0 / a)
    else if ((x * y) <= 4d+21) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (x / (a / y));
	double tmp;
	if ((x * y) <= -2e+107) {
		tmp = t_1;
	} else if ((x * y) <= -2e-8) {
		tmp = -4.5 * (z * (t / a));
	} else if ((x * y) <= -2e-25) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 4e+21) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = 0.5 * (x / (a / y))
	tmp = 0
	if (x * y) <= -2e+107:
		tmp = t_1
	elif (x * y) <= -2e-8:
		tmp = -4.5 * (z * (t / a))
	elif (x * y) <= -2e-25:
		tmp = (x * y) * (0.5 / a)
	elif (x * y) <= 4e+21:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(0.5 * Float64(x / Float64(a / y)))
	tmp = 0.0
	if (Float64(x * y) <= -2e+107)
		tmp = t_1;
	elseif (Float64(x * y) <= -2e-8)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	elseif (Float64(x * y) <= -2e-25)
		tmp = Float64(Float64(x * y) * Float64(0.5 / a));
	elseif (Float64(x * y) <= 4e+21)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = 0.5 * (x / (a / y));
	tmp = 0.0;
	if ((x * y) <= -2e+107)
		tmp = t_1;
	elseif ((x * y) <= -2e-8)
		tmp = -4.5 * (z * (t / a));
	elseif ((x * y) <= -2e-25)
		tmp = (x * y) * (0.5 / a);
	elseif ((x * y) <= 4e+21)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+107], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -2e-8], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e-25], N[(N[(x * y), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e+21], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.9999999999999999e107 or 4e21 < (*.f64 x y)

   1. Initial program 78.8%

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

      1. associate-*l* 77.9%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 77.9%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 75.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 82.9%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} \]

   7. Simplified 82.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{\frac{a}{y}}} \]

   if -1.9999999999999999e107 < (*.f64 x y) < -2e-8

   1. Initial program 88.9%

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

      1. associate-*l* 88.9%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 54.4%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 65.3%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

   7. Simplified 65.3%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t}{\frac{a}{z}}} \]
   8. Step-by-step derivation

      1. associate-/r/ 59.7%

         \[\leadsto -4.5 \cdot \color{blue}{\left(\frac{t}{a} \cdot z\right)} \]

   9. Applied egg-rr 59.7%

      \[\leadsto -4.5 \cdot \color{blue}{\left(\frac{t}{a} \cdot z\right)} \]

   if -2e-8 < (*.f64 x y) < -2.00000000000000008e-25

   1. Initial program 100.0%

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

      1. associate-*l* 100.0%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. div-inv 100.0%

         \[\leadsto \color{blue}{\left(x \cdot y - z \cdot \left(9 \cdot t\right)\right) \cdot \frac{1}{a \cdot 2}} \]

      2. fma-neg 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, -z \cdot \left(9 \cdot t\right)\right)} \cdot \frac{1}{a \cdot 2} \]

      3. *-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(x, y, -\color{blue}{\left(9 \cdot t\right) \cdot z}\right) \cdot \frac{1}{a \cdot 2} \]

      4. distribute-lft-neg-in 100.0%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(-9 \cdot t\right) \cdot z}\right) \cdot \frac{1}{a \cdot 2} \]

      5. distribute-lft-neg-in 100.0%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(\left(-9\right) \cdot t\right)} \cdot z\right) \cdot \frac{1}{a \cdot 2} \]

      6. metadata-eval 100.0%

         \[\leadsto \mathsf{fma}\left(x, y, \left(\color{blue}{-9} \cdot t\right) \cdot z\right) \cdot \frac{1}{a \cdot 2} \]

      7. *-commutative 100.0%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(t \cdot -9\right)} \cdot z\right) \cdot \frac{1}{a \cdot 2} \]

      8. add-sqr-sqrt 50.0%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(\sqrt{t \cdot -9} \cdot \sqrt{t \cdot -9}\right)} \cdot z\right) \cdot \frac{1}{a \cdot 2} \]

      9. sqrt-unprod 100.0%

         \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\sqrt{\left(t \cdot -9\right) \cdot \left(t \cdot -9\right)}} \cdot z\right) \cdot \frac{1}{a \cdot 2} \]

      10. swap-sqr 100.0%

          \[\leadsto \mathsf{fma}\left(x, y, \sqrt{\color{blue}{\left(t \cdot t\right) \cdot \left(-9 \cdot -9\right)}} \cdot z\right) \cdot \frac{1}{a \cdot 2} \]

      11. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(x, y, \sqrt{\left(t \cdot t\right) \cdot \color{blue}{81}} \cdot z\right) \cdot \frac{1}{a \cdot 2} \]

      12. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(x, y, \sqrt{\left(t \cdot t\right) \cdot \color{blue}{\left(9 \cdot 9\right)}} \cdot z\right) \cdot \frac{1}{a \cdot 2} \]

      13. swap-sqr 100.0%

          \[\leadsto \mathsf{fma}\left(x, y, \sqrt{\color{blue}{\left(t \cdot 9\right) \cdot \left(t \cdot 9\right)}} \cdot z\right) \cdot \frac{1}{a \cdot 2} \]

      14. *-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(x, y, \sqrt{\color{blue}{\left(9 \cdot t\right)} \cdot \left(t \cdot 9\right)} \cdot z\right) \cdot \frac{1}{a \cdot 2} \]

      15. *-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(x, y, \sqrt{\left(9 \cdot t\right) \cdot \color{blue}{\left(9 \cdot t\right)}} \cdot z\right) \cdot \frac{1}{a \cdot 2} \]

      16. sqrt-unprod 50.0%

          \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(\sqrt{9 \cdot t} \cdot \sqrt{9 \cdot t}\right)} \cdot z\right) \cdot \frac{1}{a \cdot 2} \]

      17. add-sqr-sqrt 91.6%

          \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(9 \cdot t\right)} \cdot z\right) \cdot \frac{1}{a \cdot 2} \]

      18. associate-*l* 91.6%

          \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{9 \cdot \left(t \cdot z\right)}\right) \cdot \frac{1}{a \cdot 2} \]

      19. *-commutative 91.6%

          \[\leadsto \mathsf{fma}\left(x, y, 9 \cdot \color{blue}{\left(z \cdot t\right)}\right) \cdot \frac{1}{a \cdot 2} \]

      20. *-commutative 91.6%

          \[\leadsto \mathsf{fma}\left(x, y, 9 \cdot \left(z \cdot t\right)\right) \cdot \frac{1}{\color{blue}{2 \cdot a}} \]

      21. associate-/r* 91.6%

          \[\leadsto \mathsf{fma}\left(x, y, 9 \cdot \left(z \cdot t\right)\right) \cdot \color{blue}{\frac{\frac{1}{2}}{a}} \]

   6. Applied egg-rr 91.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, 9 \cdot \left(z \cdot t\right)\right) \cdot \frac{0.5}{a}} \]

   7. Taylor expanded in x around inf 92.0%

      \[\leadsto \color{blue}{\left(x \cdot y\right)} \cdot \frac{0.5}{a} \]

   if -2.00000000000000008e-25 < (*.f64 x y) < 4e21

   1. Initial program 94.5%

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

      1. associate-*l* 94.5%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 94.5%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 77.5%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+107}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-8}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-25}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+21}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 94.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+304} \lor \neg \left(x \cdot y \leq 10^{+202}\right):\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y - 9 \cdot \left(z \cdot t\right)}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* x y) -2e+304) (not (<= (* x y) 1e+202)))
   (* 0.5 (/ x (/ a y)))
   (/ 0.5 (/ a (- (* x y) (* 9.0 (* z t)))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -2e+304) || !((x * y) <= 1e+202)) {
		tmp = 0.5 * (x / (a / y));
	} else {
		tmp = 0.5 / (a / ((x * y) - (9.0 * (z * t))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (((x * y) <= (-2d+304)) .or. (.not. ((x * y) <= 1d+202))) then
        tmp = 0.5d0 * (x / (a / y))
    else
        tmp = 0.5d0 / (a / ((x * y) - (9.0d0 * (z * t))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -2e+304) || !((x * y) <= 1e+202)) {
		tmp = 0.5 * (x / (a / y));
	} else {
		tmp = 0.5 / (a / ((x * y) - (9.0 * (z * t))));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if ((x * y) <= -2e+304) or not ((x * y) <= 1e+202):
		tmp = 0.5 * (x / (a / y))
	else:
		tmp = 0.5 / (a / ((x * y) - (9.0 * (z * t))))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(x * y) <= -2e+304) || !(Float64(x * y) <= 1e+202))
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	else
		tmp = Float64(0.5 / Float64(a / Float64(Float64(x * y) - Float64(9.0 * Float64(z * t)))));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x * y) <= -2e+304) || ~(((x * y) <= 1e+202)))
		tmp = 0.5 * (x / (a / y));
	else
		tmp = 0.5 / (a / ((x * y) - (9.0 * (z * t))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2e+304], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1e+202]], $MachinePrecision]], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 / N[(a / N[(N[(x * y), $MachinePrecision] - N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.9999999999999999e304 or 9.999999999999999e201 < (*.f64 x y)

   1. Initial program 58.4%

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

      1. associate-*l* 56.3%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 56.3%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 67.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 93.0%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} \]

   7. Simplified 93.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{\frac{a}{y}}} \]

   if -1.9999999999999999e304 < (*.f64 x y) < 9.999999999999999e201

   1. Initial program 94.5%

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

      1. associate-*l* 94.5%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 94.5%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 94.6%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y - 9 \cdot \left(t \cdot z\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 94.5%

         \[\leadsto \color{blue}{\frac{0.5 \cdot \left(x \cdot y - 9 \cdot \left(t \cdot z\right)\right)}{a}} \]

      2. cancel-sign-sub-inv 94.5%

         \[\leadsto \frac{0.5 \cdot \color{blue}{\left(x \cdot y + \left(-9\right) \cdot \left(t \cdot z\right)\right)}}{a} \]

      3. metadata-eval 94.5%

         \[\leadsto \frac{0.5 \cdot \left(x \cdot y + \color{blue}{-9} \cdot \left(t \cdot z\right)\right)}{a} \]

      4. +-commutative 94.5%

         \[\leadsto \frac{0.5 \cdot \color{blue}{\left(-9 \cdot \left(t \cdot z\right) + x \cdot y\right)}}{a} \]

      5. associate-/l* 94.4%

         \[\leadsto \color{blue}{\frac{0.5}{\frac{a}{-9 \cdot \left(t \cdot z\right) + x \cdot y}}} \]

      6. +-commutative 94.4%

         \[\leadsto \frac{0.5}{\frac{a}{\color{blue}{x \cdot y + -9 \cdot \left(t \cdot z\right)}}} \]

      7. metadata-eval 94.4%

         \[\leadsto \frac{0.5}{\frac{a}{x \cdot y + \color{blue}{\left(-9\right)} \cdot \left(t \cdot z\right)}} \]

      8. cancel-sign-sub-inv 94.4%

         \[\leadsto \frac{0.5}{\frac{a}{\color{blue}{x \cdot y - 9 \cdot \left(t \cdot z\right)}}} \]

      9. fma-neg 94.4%

         \[\leadsto \frac{0.5}{\frac{a}{\color{blue}{\mathsf{fma}\left(x, y, -9 \cdot \left(t \cdot z\right)\right)}}} \]

      10. *-commutative 94.4%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, -9 \cdot \color{blue}{\left(z \cdot t\right)}\right)}} \]

      11. distribute-lft-neg-in 94.4%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(-9\right) \cdot \left(z \cdot t\right)}\right)}} \]

      12. metadata-eval 94.4%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-9} \cdot \left(z \cdot t\right)\right)}} \]

      13. *-commutative 94.4%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{\left(z \cdot t\right) \cdot -9}\right)}} \]

      14. associate-*l* 94.4%

          \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(t \cdot -9\right)}\right)}} \]

   7. Simplified 94.4%

      \[\leadsto \color{blue}{\frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}}} \]
   8. Step-by-step derivation

      1. *-commutative 94.4%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(-9 \cdot t\right)}\right)}} \]

      2. metadata-eval 94.4%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \left(\color{blue}{\left(-9\right)} \cdot t\right)\right)}} \]

      3. distribute-lft-neg-in 94.4%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(-9 \cdot t\right)}\right)}} \]

      4. distribute-rgt-neg-in 94.4%

         \[\leadsto \frac{0.5}{\frac{a}{\mathsf{fma}\left(x, y, \color{blue}{-z \cdot \left(9 \cdot t\right)}\right)}} \]

      5. fma-neg 94.4%

         \[\leadsto \frac{0.5}{\frac{a}{\color{blue}{x \cdot y - z \cdot \left(9 \cdot t\right)}}} \]

      6. associate-*r* 94.4%

         \[\leadsto \frac{0.5}{\frac{a}{x \cdot y - \color{blue}{\left(z \cdot 9\right) \cdot t}}} \]

      7. *-commutative 94.4%

         \[\leadsto \frac{0.5}{\frac{a}{x \cdot y - \color{blue}{\left(9 \cdot z\right)} \cdot t}} \]

      8. associate-*l* 94.4%

         \[\leadsto \frac{0.5}{\frac{a}{x \cdot y - \color{blue}{9 \cdot \left(z \cdot t\right)}}} \]

   9. Applied egg-rr 94.4%

      \[\leadsto \frac{0.5}{\frac{a}{\color{blue}{x \cdot y - 9 \cdot \left(z \cdot t\right)}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+304} \lor \neg \left(x \cdot y \leq 10^{+202}\right):\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y - 9 \cdot \left(z \cdot t\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 95.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+304} \lor \neg \left(x \cdot y \leq 10^{+202}\right):\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* x y) -2e+304) (not (<= (* x y) 1e+202)))
   (* 0.5 (/ x (/ a y)))
   (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -2e+304) || !((x * y) <= 1e+202)) {
		tmp = 0.5 * (x / (a / y));
	} else {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (((x * y) <= (-2d+304)) .or. (.not. ((x * y) <= 1d+202))) then
        tmp = 0.5d0 * (x / (a / y))
    else
        tmp = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -2e+304) || !((x * y) <= 1e+202)) {
		tmp = 0.5 * (x / (a / y));
	} else {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if ((x * y) <= -2e+304) or not ((x * y) <= 1e+202):
		tmp = 0.5 * (x / (a / y))
	else:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(x * y) <= -2e+304) || !(Float64(x * y) <= 1e+202))
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x * y) <= -2e+304) || ~(((x * y) <= 1e+202)))
		tmp = 0.5 * (x / (a / y));
	else
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2e+304], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1e+202]], $MachinePrecision]], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.9999999999999999e304 or 9.999999999999999e201 < (*.f64 x y)

   1. Initial program 58.4%

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

      1. associate-*l* 56.3%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 56.3%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 67.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 93.0%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} \]

   7. Simplified 93.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{\frac{a}{y}}} \]

   if -1.9999999999999999e304 < (*.f64 x y) < 9.999999999999999e201

   1. Initial program 94.5%

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

      1. associate-*l* 94.5%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 94.5%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+304} \lor \neg \left(x \cdot y \leq 10^{+202}\right):\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 95.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+304} \lor \neg \left(x \cdot y \leq 10^{+202}\right):\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* x y) -2e+304) (not (<= (* x y) 1e+202)))
   (* 0.5 (/ x (/ a y)))
   (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -2e+304) || !((x * y) <= 1e+202)) {
		tmp = 0.5 * (x / (a / y));
	} else {
		tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (((x * y) <= (-2d+304)) .or. (.not. ((x * y) <= 1d+202))) then
        tmp = 0.5d0 * (x / (a / y))
    else
        tmp = ((x * y) - ((z * 9.0d0) * t)) / (a * 2.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -2e+304) || !((x * y) <= 1e+202)) {
		tmp = 0.5 * (x / (a / y));
	} else {
		tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if ((x * y) <= -2e+304) or not ((x * y) <= 1e+202):
		tmp = 0.5 * (x / (a / y))
	else:
		tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(x * y) <= -2e+304) || !(Float64(x * y) <= 1e+202))
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x * y) <= -2e+304) || ~(((x * y) <= 1e+202)))
		tmp = 0.5 * (x / (a / y));
	else
		tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2e+304], N[Not[LessEqual[N[(x * y), $MachinePrecision], 1e+202]], $MachinePrecision]], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.9999999999999999e304 or 9.999999999999999e201 < (*.f64 x y)

   1. Initial program 58.4%

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

      1. associate-*l* 56.3%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 56.3%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 67.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 93.0%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} \]

   7. Simplified 93.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{\frac{a}{y}}} \]

   if -1.9999999999999999e304 < (*.f64 x y) < 9.999999999999999e201

   1. Initial program 94.5%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+304} \lor \neg \left(x \cdot y \leq 10^{+202}\right):\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+99} \lor \neg \left(x \leq 2 \cdot 10^{-6}\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.2e+99) (not (<= x 2e-6)))
   (* 0.5 (* x (/ y a)))
   (* -4.5 (* z (/ t a)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.2e+99) || !(x <= 2e-6)) {
		tmp = 0.5 * (x * (y / a));
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((x <= (-1.2d+99)) .or. (.not. (x <= 2d-6))) then
        tmp = 0.5d0 * (x * (y / a))
    else
        tmp = (-4.5d0) * (z * (t / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.2e+99) || !(x <= 2e-6)) {
		tmp = 0.5 * (x * (y / a));
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.2e+99) or not (x <= 2e-6):
		tmp = 0.5 * (x * (y / a))
	else:
		tmp = -4.5 * (z * (t / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.2e+99) || !(x <= 2e-6))
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	else
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.2e+99) || ~((x <= 2e-6)))
		tmp = 0.5 * (x * (y / a));
	else
		tmp = -4.5 * (z * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.2e+99], N[Not[LessEqual[x, 2e-6]], $MachinePrecision]], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2000000000000001e99 or 1.99999999999999991e-6 < x

   1. Initial program 81.9%

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

      1. associate-*l* 81.1%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 81.1%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 60.8%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 66.3%

         \[\leadsto 0.5 \cdot \color{blue}{\left(x \cdot \frac{y}{a}\right)} \]

   7. Simplified 66.3%

      \[\leadsto \color{blue}{0.5 \cdot \left(x \cdot \frac{y}{a}\right)} \]

   if -1.2000000000000001e99 < x < 1.99999999999999991e-6

   1. Initial program 94.3%

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

      1. associate-*l* 94.3%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 94.3%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 72.7%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 72.0%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

   7. Simplified 72.0%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t}{\frac{a}{z}}} \]
   8. Step-by-step derivation

      1. associate-/r/ 71.3%

         \[\leadsto -4.5 \cdot \color{blue}{\left(\frac{t}{a} \cdot z\right)} \]

   9. Applied egg-rr 71.3%

      \[\leadsto -4.5 \cdot \color{blue}{\left(\frac{t}{a} \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+99} \lor \neg \left(x \leq 2 \cdot 10^{-6}\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+99}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-6}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.02e+99)
   (* 0.5 (* x (/ y a)))
   (if (<= x 1.75e-6) (* -4.5 (* z (/ t a))) (* 0.5 (/ x (/ a y))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.02e+99) {
		tmp = 0.5 * (x * (y / a));
	} else if (x <= 1.75e-6) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (x <= (-1.02d+99)) then
        tmp = 0.5d0 * (x * (y / a))
    else if (x <= 1.75d-6) then
        tmp = (-4.5d0) * (z * (t / a))
    else
        tmp = 0.5d0 * (x / (a / y))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.02e+99) {
		tmp = 0.5 * (x * (y / a));
	} else if (x <= 1.75e-6) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.02e+99:
		tmp = 0.5 * (x * (y / a))
	elif x <= 1.75e-6:
		tmp = -4.5 * (z * (t / a))
	else:
		tmp = 0.5 * (x / (a / y))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.02e+99)
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	elseif (x <= 1.75e-6)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	else
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.02e+99)
		tmp = 0.5 * (x * (y / a));
	elseif (x <= 1.75e-6)
		tmp = -4.5 * (z * (t / a));
	else
		tmp = 0.5 * (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.02e+99], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.75e-6], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.01999999999999998e99

   1. Initial program 80.8%

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

      1. associate-*l* 80.8%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 80.8%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 63.4%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-*r/ 69.9%

         \[\leadsto 0.5 \cdot \color{blue}{\left(x \cdot \frac{y}{a}\right)} \]

   7. Simplified 69.9%

      \[\leadsto \color{blue}{0.5 \cdot \left(x \cdot \frac{y}{a}\right)} \]

   if -1.01999999999999998e99 < x < 1.74999999999999997e-6

   1. Initial program 94.3%

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

      1. associate-*l* 94.3%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 94.3%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 72.7%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 72.0%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

   7. Simplified 72.0%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t}{\frac{a}{z}}} \]
   8. Step-by-step derivation

      1. associate-/r/ 71.3%

         \[\leadsto -4.5 \cdot \color{blue}{\left(\frac{t}{a} \cdot z\right)} \]

   9. Applied egg-rr 71.3%

      \[\leadsto -4.5 \cdot \color{blue}{\left(\frac{t}{a} \cdot z\right)} \]

   if 1.74999999999999997e-6 < x

   1. Initial program 82.7%

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

      1. associate-*l* 81.5%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 81.5%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 58.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 61.5%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} \]

   7. Simplified 61.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{\frac{a}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+99}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-6}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+167}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3e+167) (* -4.5 (/ t (/ a z))) (* -4.5 (/ (* z t) a))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3e+167) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (z <= (-3d+167)) then
        tmp = (-4.5d0) * (t / (a / z))
    else
        tmp = (-4.5d0) * ((z * t) / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3e+167) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -3e+167:
		tmp = -4.5 * (t / (a / z))
	else:
		tmp = -4.5 * ((z * t) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3e+167)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	else
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3e+167)
		tmp = -4.5 * (t / (a / z));
	else
		tmp = -4.5 * ((z * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3e+167], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.00000000000000012e167

   1. Initial program 66.9%

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

      1. associate-*l* 66.9%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 66.9%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 67.0%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 80.4%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

   7. Simplified 80.4%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t}{\frac{a}{z}}} \]

   if -3.00000000000000012e167 < z

   1. Initial program 91.7%

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

      1. associate-*l* 91.3%

         \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Simplified 91.3%

      \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 51.9%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+167}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ -4.5 \cdot \left(z \cdot \frac{t}{a}\right) \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a) :precision binary64 (* -4.5 (* z (/ t a))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	return -4.5 * (z * (t / a));
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    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
    code = (-4.5d0) * (z * (t / a))
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	return -4.5 * (z * (t / a));
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	return -4.5 * (z * (t / a))

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	return Float64(-4.5 * Float64(z * Float64(t / a)))
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp = code(x, y, z, t, a)
	tmp = -4.5 * (z * (t / a));
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 88.3%

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

   1. associate-*l* 88.0%

      \[\leadsto \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

3. Simplified 88.0%

   \[\leadsto \color{blue}{\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 54.0%

   \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a}} \]
6. Step-by-step derivation

   1. associate-/l* 54.7%

      \[\leadsto -4.5 \cdot \color{blue}{\frac{t}{\frac{a}{z}}} \]

7. Simplified 54.7%

   \[\leadsto \color{blue}{-4.5 \cdot \frac{t}{\frac{a}{z}}} \]
8. Step-by-step derivation

   1. associate-/r/ 54.4%

      \[\leadsto -4.5 \cdot \color{blue}{\left(\frac{t}{a} \cdot z\right)} \]

9. Applied egg-rr 54.4%

   \[\leadsto -4.5 \cdot \color{blue}{\left(\frac{t}{a} \cdot z\right)} \]

10. Final simplification 54.4%

    \[\leadsto -4.5 \cdot \left(z \cdot \frac{t}{a}\right) \]
11. Add Preprocessing

Developer target: 93.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a < -2.090464557976709 \cdot 10^{+86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a < 2.144030707833976 \cdot 10^{+99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (< a -2.090464557976709e+86)
   (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z))))
   (if (< a 2.144030707833976e+99)
     (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0))
     (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a < -2.090464557976709e+86) {
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	} else if (a < 2.144030707833976e+99) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (a < (-2.090464557976709d+86)) then
        tmp = (0.5d0 * ((y * x) / a)) - (4.5d0 * (t / (a / z)))
    else if (a < 2.144030707833976d+99) then
        tmp = ((x * y) - (z * (9.0d0 * t))) / (a * 2.0d0)
    else
        tmp = ((y / a) * (x * 0.5d0)) - ((t / a) * (z * 4.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a < -2.090464557976709e+86) {
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	} else if (a < 2.144030707833976e+99) {
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	} else {
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a < -2.090464557976709e+86:
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)))
	elif a < 2.144030707833976e+99:
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0)
	else:
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a < -2.090464557976709e+86)
		tmp = Float64(Float64(0.5 * Float64(Float64(y * x) / a)) - Float64(4.5 * Float64(t / Float64(a / z))));
	elseif (a < 2.144030707833976e+99)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(9.0 * t))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(Float64(y / a) * Float64(x * 0.5)) - Float64(Float64(t / a) * Float64(z * 4.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a < -2.090464557976709e+86)
		tmp = (0.5 * ((y * x) / a)) - (4.5 * (t / (a / z)));
	elseif (a < 2.144030707833976e+99)
		tmp = ((x * y) - (z * (9.0 * t))) / (a * 2.0);
	else
		tmp = ((y / a) * (x * 0.5)) - ((t / a) * (z * 4.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Less[a, -2.090464557976709e+86], N[(N[(0.5 * N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] - N[(4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[a, 2.144030707833976e+99], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(9.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y / a), $MachinePrecision] * N[(x * 0.5), $MachinePrecision]), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * N[(z * 4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024010 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :herbie-target
  (if (< a -2.090464557976709e+86) (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z)))) (if (< a 2.144030707833976e+99) (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0)) (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5)))))

  (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))