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

Percentage Accurate: 91.1% → 96.9%

Time: 12.8s

Alternatives: 16

Speedup: 0.6×

• 28.4% 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: 91.1% 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: 96.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := x \cdot y - t \cdot \left(z \cdot 9\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+292}:\\ \;\;\;\;\mathsf{fma}\left(0.5, \frac{y}{\frac{a}{x}}, -4.5 \cdot \left(z \cdot \frac{t}{a}\right)\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+259}:\\ \;\;\;\;\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4.5, t \cdot \frac{z}{a}, \left(0.5 \cdot y\right) \cdot \frac{x}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* t (* z 9.0)))))
   (if (<= t_1 -2e+292)
     (fma 0.5 (/ y (/ a x)) (* -4.5 (* z (/ t a))))
     (if (<= t_1 2e+259)
       (* (fma x y (* z (* t -9.0))) (/ 0.5 a))
       (fma -4.5 (* t (/ z a)) (* (* 0.5 y) (/ x a)))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (t * (z * 9.0));
	double tmp;
	if (t_1 <= -2e+292) {
		tmp = fma(0.5, (y / (a / x)), (-4.5 * (z * (t / a))));
	} else if (t_1 <= 2e+259) {
		tmp = fma(x, y, (z * (t * -9.0))) * (0.5 / a);
	} else {
		tmp = fma(-4.5, (t * (z / a)), ((0.5 * y) * (x / a)));
	}
	return tmp;
}

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(t * Float64(z * 9.0)))
	tmp = 0.0
	if (t_1 <= -2e+292)
		tmp = fma(0.5, Float64(y / Float64(a / x)), Float64(-4.5 * Float64(z * Float64(t / a))));
	elseif (t_1 <= 2e+259)
		tmp = Float64(fma(x, y, Float64(z * Float64(t * -9.0))) * Float64(0.5 / a));
	else
		tmp = fma(-4.5, Float64(t * Float64(z / a)), Float64(Float64(0.5 * y) * Float64(x / a)));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+292], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision] + N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+259], N[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision] + N[(N[(0.5 * y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < -2e292

   1. Initial program 60.1%

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

      1. associate-*l* 60.1%

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

   3. Simplified 60.1%

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

   4. Taylor expanded in x around 0 57.2%

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

      1. +-commutative 57.2%

         \[\leadsto \color{blue}{0.5 \cdot \frac{y \cdot x}{a} + -4.5 \cdot \frac{t \cdot z}{a}} \]

      2. fma-def 57.2%

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

      3. associate-/l* 78.0%

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

      4. associate-/l* 91.2%

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

      5. associate-/r/ 88.4%

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

   6. Simplified 88.4%

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

   if -2e292 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 2e259

   1. Initial program 98.6%

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

      1. associate-*l* 98.5%

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

   3. Simplified 98.5%

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

      1. div-inv 98.5%

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

      2. fma-neg 98.5%

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

      3. distribute-rgt-neg-in 98.5%

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

      4. *-commutative 98.5%

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

      5. distribute-rgt-neg-in 98.5%

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

      6. metadata-eval 98.5%

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

      7. *-commutative 98.5%

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

      8. associate-/r* 98.9%

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

      9. metadata-eval 98.9%

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

   5. Applied egg-rr 98.9%

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

   if 2e259 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 68.0%

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

      1. associate-*l* 68.0%

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

   3. Simplified 68.0%

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

      1. div-inv 68.0%

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

      2. fma-neg 70.8%

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

      3. distribute-rgt-neg-in 70.8%

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

      4. *-commutative 70.8%

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

      5. distribute-rgt-neg-in 70.8%

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

      6. metadata-eval 70.8%

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

      7. *-commutative 70.8%

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

      8. associate-/r* 70.8%

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

      9. metadata-eval 70.8%

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

   5. Applied egg-rr 70.8%

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

   6. Taylor expanded in x around 0 65.2%

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

      1. fma-def 65.2%

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

      2. *-commutative 65.2%

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

      3. associate-*l/ 73.4%

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

      4. associate-*r/ 91.7%

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

      5. associate-*l* 91.7%

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

      6. *-commutative 91.7%

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

   8. Simplified 91.7%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - t \cdot \left(z \cdot 9\right) \leq -2 \cdot 10^{+292}:\\ \;\;\;\;\mathsf{fma}\left(0.5, \frac{y}{\frac{a}{x}}, -4.5 \cdot \left(z \cdot \frac{t}{a}\right)\right)\\ \mathbf{elif}\;x \cdot y - t \cdot \left(z \cdot 9\right) \leq 2 \cdot 10^{+259}:\\ \;\;\;\;\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4.5, t \cdot \frac{z}{a}, \left(0.5 \cdot y\right) \cdot \frac{x}{a}\right)\\ \end{array} \]

Alternative 2: 93.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq -100000000:\\ \;\;\;\;\mathsf{fma}\left(-4.5, t \cdot \frac{z}{a}, \left(0.5 \cdot y\right) \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 2.0) -100000000.0)
   (fma -4.5 (* t (/ z a)) (* (* 0.5 y) (/ x a)))
   (* (fma x y (* z (* t -9.0))) (/ 0.5 a))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 2.0) <= -100000000.0) {
		tmp = fma(-4.5, (t * (z / a)), ((0.5 * y) * (x / a)));
	} else {
		tmp = fma(x, y, (z * (t * -9.0))) * (0.5 / a);
	}
	return tmp;
}

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 2.0) <= -100000000.0)
		tmp = fma(-4.5, Float64(t * Float64(z / a)), Float64(Float64(0.5 * y) * Float64(x / a)));
	else
		tmp = Float64(fma(x, y, Float64(z * Float64(t * -9.0))) * Float64(0.5 / a));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 2.0), $MachinePrecision], -100000000.0], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision] + N[(N[(0.5 * y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 2) < -1e8

   1. Initial program 74.9%

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

      1. associate-*l* 74.9%

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

   3. Simplified 74.9%

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

      1. div-inv 74.8%

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

      2. fma-neg 74.8%

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

      3. distribute-rgt-neg-in 74.8%

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

      4. *-commutative 74.8%

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

      5. distribute-rgt-neg-in 74.8%

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

      6. metadata-eval 74.8%

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

      7. *-commutative 74.8%

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

      8. associate-/r* 74.8%

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

      9. metadata-eval 74.8%

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

   5. Applied egg-rr 74.8%

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

   6. Taylor expanded in x around 0 74.9%

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

      1. fma-def 74.9%

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

      2. *-commutative 74.9%

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

      3. associate-*l/ 82.0%

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

      4. associate-*r/ 97.1%

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

      5. associate-*l* 97.1%

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

      6. *-commutative 97.1%

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

   8. Simplified 97.1%

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

   if -1e8 < (*.f64 a 2)

   1. Initial program 95.4%

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

      1. associate-*l* 95.4%

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

   3. Simplified 95.4%

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

      1. div-inv 95.3%

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

      2. fma-neg 95.9%

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

      3. distribute-rgt-neg-in 95.9%

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

      4. *-commutative 95.9%

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

      5. distribute-rgt-neg-in 95.9%

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

      6. metadata-eval 95.9%

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

      7. *-commutative 95.9%

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

      8. associate-/r* 96.4%

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

      9. metadata-eval 96.4%

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

   5. Applied egg-rr 96.4%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq -100000000:\\ \;\;\;\;\mathsf{fma}\left(-4.5, t \cdot \frac{z}{a}, \left(0.5 \cdot y\right) \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}\\ \end{array} \]

Alternative 3: 93.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq -1 \cdot 10^{-39}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{0.5 \cdot y}{a}, \left(-4.5 \cdot t\right) \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 2.0) -1e-39)
   (fma x (/ (* 0.5 y) a) (* (* -4.5 t) (/ z a)))
   (* (fma x y (* z (* t -9.0))) (/ 0.5 a))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 2.0) <= -1e-39) {
		tmp = fma(x, ((0.5 * y) / a), ((-4.5 * t) * (z / a)));
	} else {
		tmp = fma(x, y, (z * (t * -9.0))) * (0.5 / a);
	}
	return tmp;
}

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 2.0) <= -1e-39)
		tmp = fma(x, Float64(Float64(0.5 * y) / a), Float64(Float64(-4.5 * t) * Float64(z / a)));
	else
		tmp = Float64(fma(x, y, Float64(z * Float64(t * -9.0))) * Float64(0.5 / a));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 2.0), $MachinePrecision], -1e-39], N[(x * N[(N[(0.5 * y), $MachinePrecision] / a), $MachinePrecision] + N[(N[(-4.5 * t), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 2) < -9.99999999999999929e-40

   1. Initial program 76.3%

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

      1. associate-*l* 76.3%

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

   3. Simplified 76.3%

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

      1. div-inv 76.3%

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

      2. fma-neg 76.3%

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

      3. distribute-rgt-neg-in 76.3%

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

      4. *-commutative 76.3%

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

      5. distribute-rgt-neg-in 76.3%

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

      6. metadata-eval 76.3%

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

      7. *-commutative 76.3%

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

      8. associate-/r* 76.3%

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

      9. metadata-eval 76.3%

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

   5. Applied egg-rr 76.3%

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

   6. Taylor expanded in x around 0 76.4%

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

      1. fma-def 76.3%

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

      2. *-commutative 76.3%

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

      3. associate-*l/ 83.0%

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

      4. associate-*r/ 97.2%

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

      5. associate-*l* 97.2%

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

      6. *-commutative 97.2%

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

   8. Simplified 97.2%

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

      1. fma-udef 97.2%

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

      2. *-commutative 97.2%

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

      3. clear-num 97.2%

         \[\leadsto -4.5 \cdot \left(t \cdot \color{blue}{\frac{1}{\frac{a}{z}}}\right) + \frac{x}{a} \cdot \left(0.5 \cdot y\right) \]

      4. div-inv 97.2%

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

      5. associate-*r/ 97.1%

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

      6. div-inv 97.2%

         \[\leadsto \color{blue}{\left(-4.5 \cdot t\right) \cdot \frac{1}{\frac{a}{z}}} + \frac{x}{a} \cdot \left(0.5 \cdot y\right) \]

      7. clear-num 97.2%

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

   10. Applied egg-rr 97.2%

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

   11. Taylor expanded in t around 0 76.4%

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

       1. *-commutative 76.4%

          \[\leadsto -4.5 \cdot \frac{t \cdot z}{a} + \color{blue}{\frac{y \cdot x}{a} \cdot 0.5} \]

       2. associate-/r/ 76.4%

          \[\leadsto -4.5 \cdot \frac{t \cdot z}{a} + \color{blue}{\frac{y \cdot x}{\frac{a}{0.5}}} \]

       3. associate-*l/ 87.5%

          \[\leadsto -4.5 \cdot \frac{t \cdot z}{a} + \color{blue}{\frac{y}{\frac{a}{0.5}} \cdot x} \]

       4. *-commutative 87.5%

          \[\leadsto -4.5 \cdot \frac{t \cdot z}{a} + \color{blue}{x \cdot \frac{y}{\frac{a}{0.5}}} \]

       5. +-commutative 87.5%

          \[\leadsto \color{blue}{x \cdot \frac{y}{\frac{a}{0.5}} + -4.5 \cdot \frac{t \cdot z}{a}} \]

       6. fma-udef 87.5%

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

       7. associate-/l* 87.5%

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

       8. *-commutative 87.5%

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

       9. associate-*r/ 87.5%

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

       10. associate-*r* 87.5%

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

       11. associate-*r/ 95.2%

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

   13. Simplified 95.2%

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

   if -9.99999999999999929e-40 < (*.f64 a 2)

   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* 95.2%

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

   3. Simplified 95.2%

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

      1. div-inv 95.2%

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

      2. fma-neg 95.8%

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

      3. distribute-rgt-neg-in 95.8%

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

      4. *-commutative 95.8%

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

      5. distribute-rgt-neg-in 95.8%

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

      6. metadata-eval 95.8%

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

      7. *-commutative 95.8%

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

      8. associate-/r* 96.3%

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

      9. metadata-eval 96.3%

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

   5. Applied egg-rr 96.3%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq -1 \cdot 10^{-39}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{0.5 \cdot y}{a}, \left(-4.5 \cdot t\right) \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}\\ \end{array} \]

Alternative 4: 93.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq -100000000:\\ \;\;\;\;\left(-4.5 \cdot t\right) \cdot \frac{z}{a} + \left(0.5 \cdot y\right) \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 2.0) -100000000.0)
   (+ (* (* -4.5 t) (/ z a)) (* (* 0.5 y) (/ x a)))
   (* (fma x y (* z (* t -9.0))) (/ 0.5 a))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 2.0) <= -100000000.0) {
		tmp = ((-4.5 * t) * (z / a)) + ((0.5 * y) * (x / a));
	} else {
		tmp = fma(x, y, (z * (t * -9.0))) * (0.5 / a);
	}
	return tmp;
}

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 2.0) <= -100000000.0)
		tmp = Float64(Float64(Float64(-4.5 * t) * Float64(z / a)) + Float64(Float64(0.5 * y) * Float64(x / a)));
	else
		tmp = Float64(fma(x, y, Float64(z * Float64(t * -9.0))) * Float64(0.5 / a));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 2.0), $MachinePrecision], -100000000.0], N[(N[(N[(-4.5 * t), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision] + N[(N[(0.5 * y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 2) < -1e8

   1. Initial program 74.9%

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

      1. associate-*l* 74.9%

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

   3. Simplified 74.9%

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

      1. div-inv 74.8%

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

      2. fma-neg 74.8%

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

      3. distribute-rgt-neg-in 74.8%

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

      4. *-commutative 74.8%

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

      5. distribute-rgt-neg-in 74.8%

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

      6. metadata-eval 74.8%

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

      7. *-commutative 74.8%

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

      8. associate-/r* 74.8%

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

      9. metadata-eval 74.8%

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

   5. Applied egg-rr 74.8%

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

   6. Taylor expanded in x around 0 74.9%

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

      1. fma-def 74.9%

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

      2. *-commutative 74.9%

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

      3. associate-*l/ 82.0%

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

      4. associate-*r/ 97.1%

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

      5. associate-*l* 97.1%

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

      6. *-commutative 97.1%

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

   8. Simplified 97.1%

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

      1. fma-udef 97.1%

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

      2. *-commutative 97.1%

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

      3. clear-num 97.0%

         \[\leadsto -4.5 \cdot \left(t \cdot \color{blue}{\frac{1}{\frac{a}{z}}}\right) + \frac{x}{a} \cdot \left(0.5 \cdot y\right) \]

      4. div-inv 97.1%

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

      5. associate-*r/ 97.0%

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

      6. div-inv 97.0%

         \[\leadsto \color{blue}{\left(-4.5 \cdot t\right) \cdot \frac{1}{\frac{a}{z}}} + \frac{x}{a} \cdot \left(0.5 \cdot y\right) \]

      7. clear-num 97.0%

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

   10. Applied egg-rr 97.0%

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

   if -1e8 < (*.f64 a 2)

   1. Initial program 95.4%

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

      1. associate-*l* 95.4%

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

   3. Simplified 95.4%

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

      1. div-inv 95.3%

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

      2. fma-neg 95.9%

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

      3. distribute-rgt-neg-in 95.9%

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

      4. *-commutative 95.9%

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

      5. distribute-rgt-neg-in 95.9%

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

      6. metadata-eval 95.9%

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

      7. *-commutative 95.9%

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

      8. associate-/r* 96.4%

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

      9. metadata-eval 96.4%

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

   5. Applied egg-rr 96.4%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq -100000000:\\ \;\;\;\;\left(-4.5 \cdot t\right) \cdot \frac{z}{a} + \left(0.5 \cdot y\right) \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}\\ \end{array} \]

Alternative 5: 96.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := x \cdot y - t \cdot \left(z \cdot 9\right)\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+234}\right):\\ \;\;\;\;\left(-4.5 \cdot t\right) \cdot \frac{z}{a} + \left(0.5 \cdot y\right) \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* t (* z 9.0)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+234)))
     (+ (* (* -4.5 t) (/ z a)) (* (* 0.5 y) (/ x a)))
     (/ t_1 (* a 2.0)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (t * (z * 9.0));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+234)) {
		tmp = ((-4.5 * t) * (z / a)) + ((0.5 * y) * (x / a));
	} else {
		tmp = t_1 / (a * 2.0);
	}
	return tmp;
}

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (t * (z * 9.0));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+234)) {
		tmp = ((-4.5 * t) * (z / a)) + ((0.5 * y) * (x / a));
	} else {
		tmp = t_1 / (a * 2.0);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = (x * y) - (t * (z * 9.0))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+234):
		tmp = ((-4.5 * t) * (z / a)) + ((0.5 * y) * (x / a))
	else:
		tmp = t_1 / (a * 2.0)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(t * Float64(z * 9.0)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+234))
		tmp = Float64(Float64(Float64(-4.5 * t) * Float64(z / a)) + Float64(Float64(0.5 * y) * Float64(x / a)));
	else
		tmp = Float64(t_1 / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (t * (z * 9.0));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+234)))
		tmp = ((-4.5 * t) * (z / a)) + ((0.5 * y) * (x / a));
	else
		tmp = t_1 / (a * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+234]], $MachinePrecision]], N[(N[(N[(-4.5 * t), $MachinePrecision] * N[(z / a), $MachinePrecision]), $MachinePrecision] + N[(N[(0.5 * y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < -inf.0 or 2.00000000000000004e234 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 66.8%

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

      1. associate-*l* 66.8%

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

   3. Simplified 66.8%

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

      1. div-inv 66.9%

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

      2. fma-neg 68.2%

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

      3. distribute-rgt-neg-in 68.2%

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

      4. *-commutative 68.2%

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

      5. distribute-rgt-neg-in 68.2%

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

      6. metadata-eval 68.2%

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

      7. *-commutative 68.2%

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

      8. associate-/r* 68.2%

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

      9. metadata-eval 68.2%

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

   5. Applied egg-rr 68.2%

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

   6. Taylor expanded in x around 0 64.2%

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

      1. fma-def 64.2%

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

      2. *-commutative 64.2%

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

      3. associate-*l/ 72.9%

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

      4. associate-*r/ 92.1%

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

      5. associate-*l* 92.1%

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

      6. *-commutative 92.1%

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

   8. Simplified 92.1%

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

      1. fma-udef 92.1%

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

      2. *-commutative 92.1%

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

      3. clear-num 92.1%

         \[\leadsto -4.5 \cdot \left(t \cdot \color{blue}{\frac{1}{\frac{a}{z}}}\right) + \frac{x}{a} \cdot \left(0.5 \cdot y\right) \]

      4. div-inv 93.1%

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

      5. associate-*r/ 93.1%

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

      6. div-inv 92.1%

         \[\leadsto \color{blue}{\left(-4.5 \cdot t\right) \cdot \frac{1}{\frac{a}{z}}} + \frac{x}{a} \cdot \left(0.5 \cdot y\right) \]

      7. clear-num 92.1%

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

   10. Applied egg-rr 92.1%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 2.00000000000000004e234

   1. Initial program 98.5%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - t \cdot \left(z \cdot 9\right) \leq -\infty \lor \neg \left(x \cdot y - t \cdot \left(z \cdot 9\right) \leq 2 \cdot 10^{+234}\right):\\ \;\;\;\;\left(-4.5 \cdot t\right) \cdot \frac{z}{a} + \left(0.5 \cdot y\right) \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \end{array} \]

Alternative 6: 94.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\frac{0.5}{\frac{\frac{a}{y}}{x}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+211}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{0.5 \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) (- INFINITY))
   (/ 0.5 (/ (/ a y) x))
   (if (<= (* x y) 1e+211)
     (/ (- (* x y) (* z (* t 9.0))) (* a 2.0))
     (* x (/ (* 0.5 y) a)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = 0.5 / ((a / y) / x);
	} else if ((x * y) <= 1e+211) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	} else {
		tmp = x * ((0.5 * y) / a);
	}
	return tmp;
}

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = 0.5 / ((a / y) / x);
	} else if ((x * y) <= 1e+211) {
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	} else {
		tmp = x * ((0.5 * y) / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = 0.5 / ((a / y) / x)
	elif (x * y) <= 1e+211:
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0)
	else:
		tmp = x * ((0.5 * y) / a)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(0.5 / Float64(Float64(a / y) / x));
	elseif (Float64(x * y) <= 1e+211)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * Float64(t * 9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(x * Float64(Float64(0.5 * y) / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -Inf)
		tmp = 0.5 / ((a / y) / x);
	elseif ((x * y) <= 1e+211)
		tmp = ((x * y) - (z * (t * 9.0))) / (a * 2.0);
	else
		tmp = x * ((0.5 * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(0.5 / N[(N[(a / y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+211], N[(N[(N[(x * y), $MachinePrecision] - N[(z * N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(0.5 * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -inf.0

   1. Initial program 46.4%

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

      1. associate-*l* 46.4%

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

   3. Simplified 46.4%

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

   4. Taylor expanded in x around inf 46.4%

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

      1. associate-/l* 90.6%

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

   6. Simplified 90.6%

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

      1. clear-num 90.4%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{1}{\frac{\frac{a}{x}}{y}}} \]

      2. un-div-inv 90.4%

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

   8. Applied egg-rr 90.4%

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

   9. Taylor expanded in a around 0 46.4%

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

       1. associate-/r* 90.6%

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

   11. Simplified 90.6%

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

   if -inf.0 < (*.f64 x y) < 9.9999999999999996e210

   1. Initial program 95.6%

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

      1. associate-*l* 95.5%

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

   3. Simplified 95.5%

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

   if 9.9999999999999996e210 < (*.f64 x y)

   1. Initial program 70.4%

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

      1. associate-*l* 70.4%

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

   3. Simplified 70.4%

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

      1. div-inv 70.5%

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

      2. fma-neg 70.5%

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

      3. distribute-rgt-neg-in 70.5%

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

      4. *-commutative 70.5%

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

      5. distribute-rgt-neg-in 70.5%

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

      6. metadata-eval 70.5%

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

      7. *-commutative 70.5%

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

      8. associate-/r* 70.5%

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

      9. metadata-eval 70.5%

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

   5. Applied egg-rr 70.5%

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

   6. Taylor expanded in x around inf 74.3%

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

      1. associate-*r/ 74.3%

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

      2. *-commutative 74.3%

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

      3. associate-*l/ 74.3%

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

      4. *-commutative 74.3%

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

      5. associate-*l* 99.5%

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

      6. associate-*r/ 99.5%

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

      7. *-commutative 99.5%

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

   8. Simplified 99.5%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\frac{0.5}{\frac{\frac{a}{y}}{x}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+211}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(t \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{0.5 \cdot y}{a}\\ \end{array} \]

Alternative 7: 94.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\frac{0.5}{\frac{\frac{a}{y}}{x}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+211}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{0.5 \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) (- INFINITY))
   (/ 0.5 (/ (/ a y) x))
   (if (<= (* x y) 1e+211)
     (/ (- (* x y) (* t (* z 9.0))) (* a 2.0))
     (* x (/ (* 0.5 y) a)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = 0.5 / ((a / y) / x);
	} else if ((x * y) <= 1e+211) {
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0);
	} else {
		tmp = x * ((0.5 * y) / a);
	}
	return tmp;
}

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = 0.5 / ((a / y) / x);
	} else if ((x * y) <= 1e+211) {
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0);
	} else {
		tmp = x * ((0.5 * y) / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = 0.5 / ((a / y) / x)
	elif (x * y) <= 1e+211:
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0)
	else:
		tmp = x * ((0.5 * y) / a)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(0.5 / Float64(Float64(a / y) / x));
	elseif (Float64(x * y) <= 1e+211)
		tmp = Float64(Float64(Float64(x * y) - Float64(t * Float64(z * 9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(x * Float64(Float64(0.5 * y) / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -Inf)
		tmp = 0.5 / ((a / y) / x);
	elseif ((x * y) <= 1e+211)
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0);
	else
		tmp = x * ((0.5 * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(0.5 / N[(N[(a / y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+211], N[(N[(N[(x * y), $MachinePrecision] - N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(0.5 * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -inf.0

   1. Initial program 46.4%

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

      1. associate-*l* 46.4%

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

   3. Simplified 46.4%

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

   4. Taylor expanded in x around inf 46.4%

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

      1. associate-/l* 90.6%

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

   6. Simplified 90.6%

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

      1. clear-num 90.4%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{1}{\frac{\frac{a}{x}}{y}}} \]

      2. un-div-inv 90.4%

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

   8. Applied egg-rr 90.4%

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

   9. Taylor expanded in a around 0 46.4%

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

       1. associate-/r* 90.6%

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

   11. Simplified 90.6%

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

   if -inf.0 < (*.f64 x y) < 9.9999999999999996e210

   1. Initial program 95.6%

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

   if 9.9999999999999996e210 < (*.f64 x y)

   1. Initial program 70.4%

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

      1. associate-*l* 70.4%

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

   3. Simplified 70.4%

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

      1. div-inv 70.5%

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

      2. fma-neg 70.5%

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

      3. distribute-rgt-neg-in 70.5%

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

      4. *-commutative 70.5%

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

      5. distribute-rgt-neg-in 70.5%

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

      6. metadata-eval 70.5%

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

      7. *-commutative 70.5%

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

      8. associate-/r* 70.5%

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

      9. metadata-eval 70.5%

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

   5. Applied egg-rr 70.5%

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

   6. Taylor expanded in x around inf 74.3%

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

      1. associate-*r/ 74.3%

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

      2. *-commutative 74.3%

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

      3. associate-*l/ 74.3%

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

      4. *-commutative 74.3%

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

      5. associate-*l* 99.5%

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

      6. associate-*r/ 99.5%

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

      7. *-commutative 99.5%

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

   8. Simplified 99.5%

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

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\frac{0.5}{\frac{\frac{a}{y}}{x}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+211}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{0.5 \cdot y}{a}\\ \end{array} \]

Alternative 8: 66.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{0.5 \cdot y}{a}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-13}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+57} \lor \neg \left(y \leq 7 \cdot 10^{+96}\right):\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= y -6e-120)
   (* x (/ (* 0.5 y) a))
   (if (<= y 1.15e-13)
     (* -4.5 (/ (* t z) a))
     (if (or (<= y 5.4e+57) (not (<= y 7e+96)))
       (* 0.5 (/ y (/ a x)))
       (* -4.5 (/ t (/ a z)))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6e-120) {
		tmp = x * ((0.5 * y) / a);
	} else if (y <= 1.15e-13) {
		tmp = -4.5 * ((t * z) / a);
	} else if ((y <= 5.4e+57) || !(y <= 7e+96)) {
		tmp = 0.5 * (y / (a / x));
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 (y <= (-6d-120)) then
        tmp = x * ((0.5d0 * y) / a)
    else if (y <= 1.15d-13) then
        tmp = (-4.5d0) * ((t * z) / a)
    else if ((y <= 5.4d+57) .or. (.not. (y <= 7d+96))) then
        tmp = 0.5d0 * (y / (a / x))
    else
        tmp = (-4.5d0) * (t / (a / z))
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6e-120) {
		tmp = x * ((0.5 * y) / a);
	} else if (y <= 1.15e-13) {
		tmp = -4.5 * ((t * z) / a);
	} else if ((y <= 5.4e+57) || !(y <= 7e+96)) {
		tmp = 0.5 * (y / (a / x));
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if y <= -6e-120:
		tmp = x * ((0.5 * y) / a)
	elif y <= 1.15e-13:
		tmp = -4.5 * ((t * z) / a)
	elif (y <= 5.4e+57) or not (y <= 7e+96):
		tmp = 0.5 * (y / (a / x))
	else:
		tmp = -4.5 * (t / (a / z))
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -6e-120)
		tmp = Float64(x * Float64(Float64(0.5 * y) / a));
	elseif (y <= 1.15e-13)
		tmp = Float64(-4.5 * Float64(Float64(t * z) / a));
	elseif ((y <= 5.4e+57) || !(y <= 7e+96))
		tmp = Float64(0.5 * Float64(y / Float64(a / x)));
	else
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -6e-120)
		tmp = x * ((0.5 * y) / a);
	elseif (y <= 1.15e-13)
		tmp = -4.5 * ((t * z) / a);
	elseif ((y <= 5.4e+57) || ~((y <= 7e+96)))
		tmp = 0.5 * (y / (a / x));
	else
		tmp = -4.5 * (t / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[y, -6e-120], N[(x * N[(N[(0.5 * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e-13], N[(-4.5 * N[(N[(t * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 5.4e+57], N[Not[LessEqual[y, 7e+96]], $MachinePrecision]], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.00000000000000022e-120

   1. Initial program 86.9%

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

      1. associate-*l* 86.9%

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

   3. Simplified 86.9%

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

      1. div-inv 86.9%

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

      2. fma-neg 87.8%

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

      3. distribute-rgt-neg-in 87.8%

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

      4. *-commutative 87.8%

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

      5. distribute-rgt-neg-in 87.8%

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

      6. metadata-eval 87.8%

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

      7. *-commutative 87.8%

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

      8. associate-/r* 87.8%

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

      9. metadata-eval 87.8%

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

   5. Applied egg-rr 87.8%

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

   6. Taylor expanded in x around inf 50.4%

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

      1. associate-*r/ 50.4%

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

      2. *-commutative 50.4%

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

      3. associate-*l/ 50.4%

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

      4. *-commutative 50.4%

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

      5. associate-*l* 55.3%

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

      6. associate-*r/ 55.3%

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

      7. *-commutative 55.3%

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

   8. Simplified 55.3%

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

   if -6.00000000000000022e-120 < y < 1.1499999999999999e-13

   1. Initial program 95.5%

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

      1. associate-*l* 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in x around 0 76.0%

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

   if 1.1499999999999999e-13 < y < 5.3999999999999997e57 or 6.9999999999999998e96 < y

   1. Initial program 82.3%

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

      1. associate-*l* 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in x around inf 63.9%

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

      1. associate-/l* 75.9%

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

   6. Simplified 75.9%

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

   if 5.3999999999999997e57 < y < 6.9999999999999998e96

   1. Initial program 83.5%

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

      1. associate-*l* 83.3%

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

   3. Simplified 83.3%

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

   4. Taylor expanded in x around 0 53.3%

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

      1. associate-/l* 53.6%

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

   6. Simplified 53.6%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{0.5 \cdot y}{a}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-13}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+57} \lor \neg \left(y \leq 7 \cdot 10^{+96}\right):\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 9: 64.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := 0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+176}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-13}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 0.5 (/ y (/ a x)))))
   (if (<= z -2e+176)
     (* -4.5 (* z (/ t a)))
     (if (<= z -2.9e+80)
       t_1
       (if (<= z -8.5e-13)
         (* -4.5 (/ (* t z) a))
         (if (<= z 3.4e-38) t_1 (* -4.5 (/ t (/ a z)))))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (y / (a / x));
	double tmp;
	if (z <= -2e+176) {
		tmp = -4.5 * (z * (t / a));
	} else if (z <= -2.9e+80) {
		tmp = t_1;
	} else if (z <= -8.5e-13) {
		tmp = -4.5 * ((t * z) / a);
	} else if (z <= 3.4e-38) {
		tmp = t_1;
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 * (y / (a / x))
    if (z <= (-2d+176)) then
        tmp = (-4.5d0) * (z * (t / a))
    else if (z <= (-2.9d+80)) then
        tmp = t_1
    else if (z <= (-8.5d-13)) then
        tmp = (-4.5d0) * ((t * z) / a)
    else if (z <= 3.4d-38) then
        tmp = t_1
    else
        tmp = (-4.5d0) * (t / (a / z))
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (y / (a / x));
	double tmp;
	if (z <= -2e+176) {
		tmp = -4.5 * (z * (t / a));
	} else if (z <= -2.9e+80) {
		tmp = t_1;
	} else if (z <= -8.5e-13) {
		tmp = -4.5 * ((t * z) / a);
	} else if (z <= 3.4e-38) {
		tmp = t_1;
	} else {
		tmp = -4.5 * (t / (a / z));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = 0.5 * (y / (a / x))
	tmp = 0
	if z <= -2e+176:
		tmp = -4.5 * (z * (t / a))
	elif z <= -2.9e+80:
		tmp = t_1
	elif z <= -8.5e-13:
		tmp = -4.5 * ((t * z) / a)
	elif z <= 3.4e-38:
		tmp = t_1
	else:
		tmp = -4.5 * (t / (a / z))
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(0.5 * Float64(y / Float64(a / x)))
	tmp = 0.0
	if (z <= -2e+176)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	elseif (z <= -2.9e+80)
		tmp = t_1;
	elseif (z <= -8.5e-13)
		tmp = Float64(-4.5 * Float64(Float64(t * z) / a));
	elseif (z <= 3.4e-38)
		tmp = t_1;
	else
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = 0.5 * (y / (a / x));
	tmp = 0.0;
	if (z <= -2e+176)
		tmp = -4.5 * (z * (t / a));
	elseif (z <= -2.9e+80)
		tmp = t_1;
	elseif (z <= -8.5e-13)
		tmp = -4.5 * ((t * z) / a);
	elseif (z <= 3.4e-38)
		tmp = t_1;
	else
		tmp = -4.5 * (t / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+176], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.9e+80], t$95$1, If[LessEqual[z, -8.5e-13], N[(-4.5 * N[(N[(t * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e-38], t$95$1, N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2e176

   1. Initial program 85.5%

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

      1. associate-*l* 85.4%

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

   3. Simplified 85.4%

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

   4. Taylor expanded in x around 0 82.5%

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

      1. associate-/l* 82.6%

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

      2. associate-/r/ 89.3%

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

   6. Simplified 89.3%

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

   if -2e176 < z < -2.89999999999999986e80 or -8.5000000000000001e-13 < z < 3.4000000000000002e-38

   1. Initial program 90.8%

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

      1. associate-*l* 90.7%

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

   3. Simplified 90.7%

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

   4. Taylor expanded in x around inf 59.2%

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

      1. associate-/l* 64.7%

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

   6. Simplified 64.7%

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

   if -2.89999999999999986e80 < z < -8.5000000000000001e-13

   1. Initial program 95.0%

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

      1. associate-*l* 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in x around 0 76.5%

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

   if 3.4000000000000002e-38 < z

   1. Initial program 85.1%

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

      1. associate-*l* 85.1%

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

   3. Simplified 85.1%

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

   4. Taylor expanded in x around 0 51.2%

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

      1. associate-/l* 56.3%

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

   6. Simplified 56.3%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+176}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+80}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-13}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-38}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 10: 66.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{0.5 \cdot y}{a}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-12}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+63}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+96}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(0.5 \cdot y\right) \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.9e-120)
   (* x (/ (* 0.5 y) a))
   (if (<= y 1.1e-12)
     (* -4.5 (/ (* t z) a))
     (if (<= y 1.26e+63)
       (* 0.5 (/ y (/ a x)))
       (if (<= y 7.5e+96) (* -4.5 (/ t (/ a z))) (* (* 0.5 y) (/ x a)))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.9e-120) {
		tmp = x * ((0.5 * y) / a);
	} else if (y <= 1.1e-12) {
		tmp = -4.5 * ((t * z) / a);
	} else if (y <= 1.26e+63) {
		tmp = 0.5 * (y / (a / x));
	} else if (y <= 7.5e+96) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = (0.5 * y) * (x / a);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 (y <= (-2.9d-120)) then
        tmp = x * ((0.5d0 * y) / a)
    else if (y <= 1.1d-12) then
        tmp = (-4.5d0) * ((t * z) / a)
    else if (y <= 1.26d+63) then
        tmp = 0.5d0 * (y / (a / x))
    else if (y <= 7.5d+96) then
        tmp = (-4.5d0) * (t / (a / z))
    else
        tmp = (0.5d0 * y) * (x / a)
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.9e-120) {
		tmp = x * ((0.5 * y) / a);
	} else if (y <= 1.1e-12) {
		tmp = -4.5 * ((t * z) / a);
	} else if (y <= 1.26e+63) {
		tmp = 0.5 * (y / (a / x));
	} else if (y <= 7.5e+96) {
		tmp = -4.5 * (t / (a / z));
	} else {
		tmp = (0.5 * y) * (x / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.9e-120:
		tmp = x * ((0.5 * y) / a)
	elif y <= 1.1e-12:
		tmp = -4.5 * ((t * z) / a)
	elif y <= 1.26e+63:
		tmp = 0.5 * (y / (a / x))
	elif y <= 7.5e+96:
		tmp = -4.5 * (t / (a / z))
	else:
		tmp = (0.5 * y) * (x / a)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.9e-120)
		tmp = Float64(x * Float64(Float64(0.5 * y) / a));
	elseif (y <= 1.1e-12)
		tmp = Float64(-4.5 * Float64(Float64(t * z) / a));
	elseif (y <= 1.26e+63)
		tmp = Float64(0.5 * Float64(y / Float64(a / x)));
	elseif (y <= 7.5e+96)
		tmp = Float64(-4.5 * Float64(t / Float64(a / z)));
	else
		tmp = Float64(Float64(0.5 * y) * Float64(x / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.9e-120)
		tmp = x * ((0.5 * y) / a);
	elseif (y <= 1.1e-12)
		tmp = -4.5 * ((t * z) / a);
	elseif (y <= 1.26e+63)
		tmp = 0.5 * (y / (a / x));
	elseif (y <= 7.5e+96)
		tmp = -4.5 * (t / (a / z));
	else
		tmp = (0.5 * y) * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.9e-120], N[(x * N[(N[(0.5 * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e-12], N[(-4.5 * N[(N[(t * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.26e+63], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+96], N[(-4.5 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 * y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.9e-120

   1. Initial program 86.9%

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

      1. associate-*l* 86.9%

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

   3. Simplified 86.9%

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

      1. div-inv 86.9%

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

      2. fma-neg 87.8%

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

      3. distribute-rgt-neg-in 87.8%

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

      4. *-commutative 87.8%

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

      5. distribute-rgt-neg-in 87.8%

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

      6. metadata-eval 87.8%

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

      7. *-commutative 87.8%

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

      8. associate-/r* 87.8%

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

      9. metadata-eval 87.8%

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

   5. Applied egg-rr 87.8%

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

   6. Taylor expanded in x around inf 50.4%

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

      1. associate-*r/ 50.4%

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

      2. *-commutative 50.4%

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

      3. associate-*l/ 50.4%

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

      4. *-commutative 50.4%

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

      5. associate-*l* 55.3%

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

      6. associate-*r/ 55.3%

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

      7. *-commutative 55.3%

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

   8. Simplified 55.3%

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

   if -2.9e-120 < y < 1.09999999999999996e-12

   1. Initial program 95.5%

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

      1. associate-*l* 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in x around 0 76.0%

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

   if 1.09999999999999996e-12 < y < 1.26e63

   1. Initial program 93.0%

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

      1. associate-*l* 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in x around inf 64.0%

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

      1. associate-/l* 70.0%

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

   6. Simplified 70.0%

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

   if 1.26e63 < y < 7.4999999999999996e96

   1. Initial program 83.5%

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

      1. associate-*l* 83.3%

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

   3. Simplified 83.3%

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

   4. Taylor expanded in x around 0 53.3%

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

      1. associate-/l* 53.6%

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

   6. Simplified 53.6%

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

   if 7.4999999999999996e96 < y

   1. Initial program 78.6%

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

      1. associate-*l* 78.5%

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

   3. Simplified 78.5%

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

      1. div-inv 78.6%

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

      2. fma-neg 78.6%

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

      3. distribute-rgt-neg-in 78.6%

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

      4. *-commutative 78.6%

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

      5. distribute-rgt-neg-in 78.6%

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

      6. metadata-eval 78.6%

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

      7. *-commutative 78.6%

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

      8. associate-/r* 78.6%

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

      9. metadata-eval 78.6%

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

   5. Applied egg-rr 78.6%

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

   6. Taylor expanded in x around inf 63.9%

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

      1. associate-*r/ 77.8%

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

      2. associate-*l* 77.8%

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

      3. *-commutative 77.8%

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

   8. Simplified 77.8%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \left(0.5 \cdot y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{0.5 \cdot y}{a}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-12}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+63}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+96}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\left(0.5 \cdot y\right) \cdot \frac{x}{a}\\ \end{array} \]

Alternative 11: 66.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{0.5 \cdot y}{a}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-12}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+63}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+96}:\\ \;\;\;\;\frac{-4.5}{\frac{\frac{a}{z}}{t}}\\ \mathbf{else}:\\ \;\;\;\;\left(0.5 \cdot y\right) \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= y -6e-120)
   (* x (/ (* 0.5 y) a))
   (if (<= y 8e-12)
     (* -4.5 (/ (* t z) a))
     (if (<= y 7.2e+63)
       (* 0.5 (/ y (/ a x)))
       (if (<= y 7e+96) (/ -4.5 (/ (/ a z) t)) (* (* 0.5 y) (/ x a)))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6e-120) {
		tmp = x * ((0.5 * y) / a);
	} else if (y <= 8e-12) {
		tmp = -4.5 * ((t * z) / a);
	} else if (y <= 7.2e+63) {
		tmp = 0.5 * (y / (a / x));
	} else if (y <= 7e+96) {
		tmp = -4.5 / ((a / z) / t);
	} else {
		tmp = (0.5 * y) * (x / a);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 (y <= (-6d-120)) then
        tmp = x * ((0.5d0 * y) / a)
    else if (y <= 8d-12) then
        tmp = (-4.5d0) * ((t * z) / a)
    else if (y <= 7.2d+63) then
        tmp = 0.5d0 * (y / (a / x))
    else if (y <= 7d+96) then
        tmp = (-4.5d0) / ((a / z) / t)
    else
        tmp = (0.5d0 * y) * (x / a)
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6e-120) {
		tmp = x * ((0.5 * y) / a);
	} else if (y <= 8e-12) {
		tmp = -4.5 * ((t * z) / a);
	} else if (y <= 7.2e+63) {
		tmp = 0.5 * (y / (a / x));
	} else if (y <= 7e+96) {
		tmp = -4.5 / ((a / z) / t);
	} else {
		tmp = (0.5 * y) * (x / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if y <= -6e-120:
		tmp = x * ((0.5 * y) / a)
	elif y <= 8e-12:
		tmp = -4.5 * ((t * z) / a)
	elif y <= 7.2e+63:
		tmp = 0.5 * (y / (a / x))
	elif y <= 7e+96:
		tmp = -4.5 / ((a / z) / t)
	else:
		tmp = (0.5 * y) * (x / a)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -6e-120)
		tmp = Float64(x * Float64(Float64(0.5 * y) / a));
	elseif (y <= 8e-12)
		tmp = Float64(-4.5 * Float64(Float64(t * z) / a));
	elseif (y <= 7.2e+63)
		tmp = Float64(0.5 * Float64(y / Float64(a / x)));
	elseif (y <= 7e+96)
		tmp = Float64(-4.5 / Float64(Float64(a / z) / t));
	else
		tmp = Float64(Float64(0.5 * y) * Float64(x / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -6e-120)
		tmp = x * ((0.5 * y) / a);
	elseif (y <= 8e-12)
		tmp = -4.5 * ((t * z) / a);
	elseif (y <= 7.2e+63)
		tmp = 0.5 * (y / (a / x));
	elseif (y <= 7e+96)
		tmp = -4.5 / ((a / z) / t);
	else
		tmp = (0.5 * y) * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[y, -6e-120], N[(x * N[(N[(0.5 * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e-12], N[(-4.5 * N[(N[(t * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e+63], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+96], N[(-4.5 / N[(N[(a / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 * y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.00000000000000022e-120

   1. Initial program 86.9%

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

      1. associate-*l* 86.9%

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

   3. Simplified 86.9%

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

      1. div-inv 86.9%

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

      2. fma-neg 87.8%

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

      3. distribute-rgt-neg-in 87.8%

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

      4. *-commutative 87.8%

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

      5. distribute-rgt-neg-in 87.8%

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

      6. metadata-eval 87.8%

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

      7. *-commutative 87.8%

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

      8. associate-/r* 87.8%

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

      9. metadata-eval 87.8%

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

   5. Applied egg-rr 87.8%

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

   6. Taylor expanded in x around inf 50.4%

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

      1. associate-*r/ 50.4%

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

      2. *-commutative 50.4%

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

      3. associate-*l/ 50.4%

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

      4. *-commutative 50.4%

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

      5. associate-*l* 55.3%

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

      6. associate-*r/ 55.3%

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

      7. *-commutative 55.3%

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

   8. Simplified 55.3%

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

   if -6.00000000000000022e-120 < y < 7.99999999999999984e-12

   1. Initial program 95.5%

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

      1. associate-*l* 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in x around 0 76.0%

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

   if 7.99999999999999984e-12 < y < 7.19999999999999998e63

   1. Initial program 93.0%

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

      1. associate-*l* 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in x around inf 64.0%

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

      1. associate-/l* 70.0%

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

   6. Simplified 70.0%

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

   if 7.19999999999999998e63 < y < 6.9999999999999998e96

   1. Initial program 83.5%

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

      1. associate-*l* 83.3%

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

   3. Simplified 83.3%

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

   4. Taylor expanded in x around 0 53.3%

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

      1. associate-/l* 53.6%

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

   6. Simplified 53.6%

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

      1. clear-num 53.6%

         \[\leadsto -4.5 \cdot \color{blue}{\frac{1}{\frac{\frac{a}{z}}{t}}} \]

      2. un-div-inv 53.4%

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

   8. Applied egg-rr 53.4%

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

   if 6.9999999999999998e96 < y

   1. Initial program 78.6%

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

      1. associate-*l* 78.5%

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

   3. Simplified 78.5%

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

      1. div-inv 78.6%

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

      2. fma-neg 78.6%

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

      3. distribute-rgt-neg-in 78.6%

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

      4. *-commutative 78.6%

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

      5. distribute-rgt-neg-in 78.6%

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

      6. metadata-eval 78.6%

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

      7. *-commutative 78.6%

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

      8. associate-/r* 78.6%

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

      9. metadata-eval 78.6%

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

   5. Applied egg-rr 78.6%

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

   6. Taylor expanded in x around inf 63.9%

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

      1. associate-*r/ 77.8%

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

      2. associate-*l* 77.8%

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

      3. *-commutative 77.8%

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

   8. Simplified 77.8%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \left(0.5 \cdot y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{0.5 \cdot y}{a}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-12}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+63}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+96}:\\ \;\;\;\;\frac{-4.5}{\frac{\frac{a}{z}}{t}}\\ \mathbf{else}:\\ \;\;\;\;\left(0.5 \cdot y\right) \cdot \frac{x}{a}\\ \end{array} \]

Alternative 12: 66.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{0.5 \cdot y}{a}\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{-13}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+63}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+96}:\\ \;\;\;\;\frac{z}{-0.2222222222222222 \cdot \frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\left(0.5 \cdot y\right) \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= y -6e-120)
   (* x (/ (* 0.5 y) a))
   (if (<= y 1.46e-13)
     (* -4.5 (/ (* t z) a))
     (if (<= y 1.26e+63)
       (* 0.5 (/ y (/ a x)))
       (if (<= y 7e+96)
         (/ z (* -0.2222222222222222 (/ a t)))
         (* (* 0.5 y) (/ x a)))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6e-120) {
		tmp = x * ((0.5 * y) / a);
	} else if (y <= 1.46e-13) {
		tmp = -4.5 * ((t * z) / a);
	} else if (y <= 1.26e+63) {
		tmp = 0.5 * (y / (a / x));
	} else if (y <= 7e+96) {
		tmp = z / (-0.2222222222222222 * (a / t));
	} else {
		tmp = (0.5 * y) * (x / a);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 (y <= (-6d-120)) then
        tmp = x * ((0.5d0 * y) / a)
    else if (y <= 1.46d-13) then
        tmp = (-4.5d0) * ((t * z) / a)
    else if (y <= 1.26d+63) then
        tmp = 0.5d0 * (y / (a / x))
    else if (y <= 7d+96) then
        tmp = z / ((-0.2222222222222222d0) * (a / t))
    else
        tmp = (0.5d0 * y) * (x / a)
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6e-120) {
		tmp = x * ((0.5 * y) / a);
	} else if (y <= 1.46e-13) {
		tmp = -4.5 * ((t * z) / a);
	} else if (y <= 1.26e+63) {
		tmp = 0.5 * (y / (a / x));
	} else if (y <= 7e+96) {
		tmp = z / (-0.2222222222222222 * (a / t));
	} else {
		tmp = (0.5 * y) * (x / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if y <= -6e-120:
		tmp = x * ((0.5 * y) / a)
	elif y <= 1.46e-13:
		tmp = -4.5 * ((t * z) / a)
	elif y <= 1.26e+63:
		tmp = 0.5 * (y / (a / x))
	elif y <= 7e+96:
		tmp = z / (-0.2222222222222222 * (a / t))
	else:
		tmp = (0.5 * y) * (x / a)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -6e-120)
		tmp = Float64(x * Float64(Float64(0.5 * y) / a));
	elseif (y <= 1.46e-13)
		tmp = Float64(-4.5 * Float64(Float64(t * z) / a));
	elseif (y <= 1.26e+63)
		tmp = Float64(0.5 * Float64(y / Float64(a / x)));
	elseif (y <= 7e+96)
		tmp = Float64(z / Float64(-0.2222222222222222 * Float64(a / t)));
	else
		tmp = Float64(Float64(0.5 * y) * Float64(x / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -6e-120)
		tmp = x * ((0.5 * y) / a);
	elseif (y <= 1.46e-13)
		tmp = -4.5 * ((t * z) / a);
	elseif (y <= 1.26e+63)
		tmp = 0.5 * (y / (a / x));
	elseif (y <= 7e+96)
		tmp = z / (-0.2222222222222222 * (a / t));
	else
		tmp = (0.5 * y) * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[y, -6e-120], N[(x * N[(N[(0.5 * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.46e-13], N[(-4.5 * N[(N[(t * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.26e+63], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+96], N[(z / N[(-0.2222222222222222 * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 * y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.00000000000000022e-120

   1. Initial program 86.9%

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

      1. associate-*l* 86.9%

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

   3. Simplified 86.9%

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

      1. div-inv 86.9%

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

      2. fma-neg 87.8%

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

      3. distribute-rgt-neg-in 87.8%

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

      4. *-commutative 87.8%

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

      5. distribute-rgt-neg-in 87.8%

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

      6. metadata-eval 87.8%

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

      7. *-commutative 87.8%

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

      8. associate-/r* 87.8%

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

      9. metadata-eval 87.8%

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

   5. Applied egg-rr 87.8%

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

   6. Taylor expanded in x around inf 50.4%

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

      1. associate-*r/ 50.4%

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

      2. *-commutative 50.4%

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

      3. associate-*l/ 50.4%

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

      4. *-commutative 50.4%

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

      5. associate-*l* 55.3%

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

      6. associate-*r/ 55.3%

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

      7. *-commutative 55.3%

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

   8. Simplified 55.3%

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

   if -6.00000000000000022e-120 < y < 1.46000000000000009e-13

   1. Initial program 95.5%

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

      1. associate-*l* 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in x around 0 76.0%

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

   if 1.46000000000000009e-13 < y < 1.26e63

   1. Initial program 93.0%

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

      1. associate-*l* 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in x around inf 64.0%

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

      1. associate-/l* 70.0%

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

   6. Simplified 70.0%

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

   if 1.26e63 < y < 6.9999999999999998e96

   1. Initial program 83.5%

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

      1. associate-*l* 83.3%

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

   3. Simplified 83.3%

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

   4. Taylor expanded in x around 0 53.3%

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

      1. *-commutative 53.3%

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

      2. *-commutative 53.3%

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

      3. associate-*r* 53.1%

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

   6. Simplified 53.1%

      \[\leadsto \frac{\color{blue}{z \cdot \left(t \cdot -9\right)}}{a \cdot 2} \]
   7. Step-by-step derivation

      1. associate-/l* 65.9%

         \[\leadsto \color{blue}{\frac{z}{\frac{a \cdot 2}{t \cdot -9}}} \]

      2. div-inv 51.6%

         \[\leadsto \color{blue}{z \cdot \frac{1}{\frac{a \cdot 2}{t \cdot -9}}} \]

      3. times-frac 52.1%

         \[\leadsto z \cdot \frac{1}{\color{blue}{\frac{a}{t} \cdot \frac{2}{-9}}} \]

      4. metadata-eval 52.1%

         \[\leadsto z \cdot \frac{1}{\frac{a}{t} \cdot \color{blue}{-0.2222222222222222}} \]

   8. Applied egg-rr 52.1%

      \[\leadsto \color{blue}{z \cdot \frac{1}{\frac{a}{t} \cdot -0.2222222222222222}} \]
   9. Step-by-step derivation

      1. associate-*r/ 66.2%

         \[\leadsto \color{blue}{\frac{z \cdot 1}{\frac{a}{t} \cdot -0.2222222222222222}} \]

      2. *-rgt-identity 66.2%

         \[\leadsto \frac{\color{blue}{z}}{\frac{a}{t} \cdot -0.2222222222222222} \]

      3. *-commutative 66.2%

         \[\leadsto \frac{z}{\color{blue}{-0.2222222222222222 \cdot \frac{a}{t}}} \]

   10. Simplified 66.2%

       \[\leadsto \color{blue}{\frac{z}{-0.2222222222222222 \cdot \frac{a}{t}}} \]

   if 6.9999999999999998e96 < y

   1. Initial program 78.6%

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

      1. associate-*l* 78.5%

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

   3. Simplified 78.5%

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

      1. div-inv 78.6%

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

      2. fma-neg 78.6%

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

      3. distribute-rgt-neg-in 78.6%

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

      4. *-commutative 78.6%

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

      5. distribute-rgt-neg-in 78.6%

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

      6. metadata-eval 78.6%

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

      7. *-commutative 78.6%

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

      8. associate-/r* 78.6%

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

      9. metadata-eval 78.6%

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

   5. Applied egg-rr 78.6%

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

   6. Taylor expanded in x around inf 63.9%

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

      1. associate-*r/ 77.8%

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

      2. associate-*l* 77.8%

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

      3. *-commutative 77.8%

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

   8. Simplified 77.8%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \left(0.5 \cdot y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{0.5 \cdot y}{a}\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{-13}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+63}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+96}:\\ \;\;\;\;\frac{z}{-0.2222222222222222 \cdot \frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\left(0.5 \cdot y\right) \cdot \frac{x}{a}\\ \end{array} \]

Alternative 13: 66.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{0.5 \cdot y}{a}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-13}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+63}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{+97}:\\ \;\;\;\;\frac{z}{-0.2222222222222222 \cdot \frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\left(0.5 \cdot y\right) \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5.9e-120)
   (* x (/ (* 0.5 y) a))
   (if (<= y 1.75e-13)
     (* -4.5 (/ (* t z) a))
     (if (<= y 6.6e+63)
       (/ (* x y) (* a 2.0))
       (if (<= y 1.42e+97)
         (/ z (* -0.2222222222222222 (/ a t)))
         (* (* 0.5 y) (/ x a)))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.9e-120) {
		tmp = x * ((0.5 * y) / a);
	} else if (y <= 1.75e-13) {
		tmp = -4.5 * ((t * z) / a);
	} else if (y <= 6.6e+63) {
		tmp = (x * y) / (a * 2.0);
	} else if (y <= 1.42e+97) {
		tmp = z / (-0.2222222222222222 * (a / t));
	} else {
		tmp = (0.5 * y) * (x / a);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 (y <= (-5.9d-120)) then
        tmp = x * ((0.5d0 * y) / a)
    else if (y <= 1.75d-13) then
        tmp = (-4.5d0) * ((t * z) / a)
    else if (y <= 6.6d+63) then
        tmp = (x * y) / (a * 2.0d0)
    else if (y <= 1.42d+97) then
        tmp = z / ((-0.2222222222222222d0) * (a / t))
    else
        tmp = (0.5d0 * y) * (x / a)
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.9e-120) {
		tmp = x * ((0.5 * y) / a);
	} else if (y <= 1.75e-13) {
		tmp = -4.5 * ((t * z) / a);
	} else if (y <= 6.6e+63) {
		tmp = (x * y) / (a * 2.0);
	} else if (y <= 1.42e+97) {
		tmp = z / (-0.2222222222222222 * (a / t));
	} else {
		tmp = (0.5 * y) * (x / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if y <= -5.9e-120:
		tmp = x * ((0.5 * y) / a)
	elif y <= 1.75e-13:
		tmp = -4.5 * ((t * z) / a)
	elif y <= 6.6e+63:
		tmp = (x * y) / (a * 2.0)
	elif y <= 1.42e+97:
		tmp = z / (-0.2222222222222222 * (a / t))
	else:
		tmp = (0.5 * y) * (x / a)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5.9e-120)
		tmp = Float64(x * Float64(Float64(0.5 * y) / a));
	elseif (y <= 1.75e-13)
		tmp = Float64(-4.5 * Float64(Float64(t * z) / a));
	elseif (y <= 6.6e+63)
		tmp = Float64(Float64(x * y) / Float64(a * 2.0));
	elseif (y <= 1.42e+97)
		tmp = Float64(z / Float64(-0.2222222222222222 * Float64(a / t)));
	else
		tmp = Float64(Float64(0.5 * y) * Float64(x / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -5.9e-120)
		tmp = x * ((0.5 * y) / a);
	elseif (y <= 1.75e-13)
		tmp = -4.5 * ((t * z) / a);
	elseif (y <= 6.6e+63)
		tmp = (x * y) / (a * 2.0);
	elseif (y <= 1.42e+97)
		tmp = z / (-0.2222222222222222 * (a / t));
	else
		tmp = (0.5 * y) * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[y, -5.9e-120], N[(x * N[(N[(0.5 * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e-13], N[(-4.5 * N[(N[(t * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.6e+63], N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.42e+97], N[(z / N[(-0.2222222222222222 * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 * y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -5.89999999999999979e-120

   1. Initial program 86.9%

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

      1. associate-*l* 86.9%

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

   3. Simplified 86.9%

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

      1. div-inv 86.9%

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

      2. fma-neg 87.8%

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

      3. distribute-rgt-neg-in 87.8%

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

      4. *-commutative 87.8%

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

      5. distribute-rgt-neg-in 87.8%

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

      6. metadata-eval 87.8%

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

      7. *-commutative 87.8%

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

      8. associate-/r* 87.8%

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

      9. metadata-eval 87.8%

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

   5. Applied egg-rr 87.8%

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

   6. Taylor expanded in x around inf 50.4%

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

      1. associate-*r/ 50.4%

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

      2. *-commutative 50.4%

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

      3. associate-*l/ 50.4%

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

      4. *-commutative 50.4%

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

      5. associate-*l* 55.3%

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

      6. associate-*r/ 55.3%

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

      7. *-commutative 55.3%

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

   8. Simplified 55.3%

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

   if -5.89999999999999979e-120 < y < 1.7500000000000001e-13

   1. Initial program 95.5%

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

      1. associate-*l* 95.5%

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

   3. Simplified 95.5%

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

   4. Taylor expanded in x around 0 76.0%

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

   if 1.7500000000000001e-13 < y < 6.6000000000000003e63

   1. Initial program 93.0%

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

      1. associate-*l* 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in x around inf 64.0%

      \[\leadsto \frac{\color{blue}{y \cdot x}}{a \cdot 2} \]

   if 6.6000000000000003e63 < y < 1.41999999999999991e97

   1. Initial program 83.5%

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

      1. associate-*l* 83.3%

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

   3. Simplified 83.3%

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

   4. Taylor expanded in x around 0 53.3%

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

      1. *-commutative 53.3%

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

      2. *-commutative 53.3%

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

      3. associate-*r* 53.1%

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

   6. Simplified 53.1%

      \[\leadsto \frac{\color{blue}{z \cdot \left(t \cdot -9\right)}}{a \cdot 2} \]
   7. Step-by-step derivation

      1. associate-/l* 65.9%

         \[\leadsto \color{blue}{\frac{z}{\frac{a \cdot 2}{t \cdot -9}}} \]

      2. div-inv 51.6%

         \[\leadsto \color{blue}{z \cdot \frac{1}{\frac{a \cdot 2}{t \cdot -9}}} \]

      3. times-frac 52.1%

         \[\leadsto z \cdot \frac{1}{\color{blue}{\frac{a}{t} \cdot \frac{2}{-9}}} \]

      4. metadata-eval 52.1%

         \[\leadsto z \cdot \frac{1}{\frac{a}{t} \cdot \color{blue}{-0.2222222222222222}} \]

   8. Applied egg-rr 52.1%

      \[\leadsto \color{blue}{z \cdot \frac{1}{\frac{a}{t} \cdot -0.2222222222222222}} \]
   9. Step-by-step derivation

      1. associate-*r/ 66.2%

         \[\leadsto \color{blue}{\frac{z \cdot 1}{\frac{a}{t} \cdot -0.2222222222222222}} \]

      2. *-rgt-identity 66.2%

         \[\leadsto \frac{\color{blue}{z}}{\frac{a}{t} \cdot -0.2222222222222222} \]

      3. *-commutative 66.2%

         \[\leadsto \frac{z}{\color{blue}{-0.2222222222222222 \cdot \frac{a}{t}}} \]

   10. Simplified 66.2%

       \[\leadsto \color{blue}{\frac{z}{-0.2222222222222222 \cdot \frac{a}{t}}} \]

   if 1.41999999999999991e97 < y

   1. Initial program 78.6%

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

      1. associate-*l* 78.5%

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

   3. Simplified 78.5%

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

      1. div-inv 78.6%

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

      2. fma-neg 78.6%

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

      3. distribute-rgt-neg-in 78.6%

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

      4. *-commutative 78.6%

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

      5. distribute-rgt-neg-in 78.6%

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

      6. metadata-eval 78.6%

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

      7. *-commutative 78.6%

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

      8. associate-/r* 78.6%

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

      9. metadata-eval 78.6%

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

   5. Applied egg-rr 78.6%

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

   6. Taylor expanded in x around inf 63.9%

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

      1. associate-*r/ 77.8%

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

      2. associate-*l* 77.8%

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

      3. *-commutative 77.8%

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

   8. Simplified 77.8%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \left(0.5 \cdot y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \frac{0.5 \cdot y}{a}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-13}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+63}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{+97}:\\ \;\;\;\;\frac{z}{-0.2222222222222222 \cdot \frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\left(0.5 \cdot y\right) \cdot \frac{x}{a}\\ \end{array} \]

Alternative 14: 51.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+51}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.6e+51) (* -4.5 (* z (/ t a))) (* -4.5 (/ (* t z) a))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.6e+51) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = -4.5 * ((t * z) / a);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 (a <= (-5.6d+51)) then
        tmp = (-4.5d0) * (z * (t / a))
    else
        tmp = (-4.5d0) * ((t * z) / a)
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.6e+51) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = -4.5 * ((t * z) / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.6e+51:
		tmp = -4.5 * (z * (t / a))
	else:
		tmp = -4.5 * ((t * z) / a)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.6e+51)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	else
		tmp = Float64(-4.5 * Float64(Float64(t * z) / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.6e+51)
		tmp = -4.5 * (z * (t / a));
	else
		tmp = -4.5 * ((t * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.6e+51], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(t * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.60000000000000009e51

   1. Initial program 71.9%

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

      1. associate-*l* 71.9%

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

   3. Simplified 71.9%

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

   4. Taylor expanded in x around 0 41.9%

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

      1. associate-/l* 50.1%

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

      2. associate-/r/ 50.8%

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

   6. Simplified 50.8%

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

   if -5.60000000000000009e51 < a

   1. Initial program 95.2%

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

      1. associate-*l* 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in x around 0 52.6%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+51}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t \cdot z}{a}\\ \end{array} \]

Alternative 15: 51.4% accurate, 1.9× speedup

Math

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

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	return -4.5 * (z * (t / a));
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	return -4.5 * (z * (t / a));
}

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 89.0%

   \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
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. Taylor expanded in x around 0 49.7%

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

   1. associate-/l* 49.2%

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

   2. associate-/r/ 48.8%

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

6. Simplified 48.8%

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

7. Final simplification 48.8%

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

Alternative 16: 51.1% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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) * (t / (a / z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.0%

   \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
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. Taylor expanded in x around 0 49.7%

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

   1. associate-/l* 49.2%

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

6. Simplified 49.2%

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

7. Final simplification 49.2%

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

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 2023274 
(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)))