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

Percentage Accurate: 91.4% → 96.9%

Time: 9.8s

Alternatives: 7

Speedup: 0.6×

• 28.0% 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: 91.4% 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

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+253}\right):\\ \;\;\;\;\mathsf{fma}\left(-4.5, z \cdot \frac{t}{a}, 0.5 \cdot \frac{y}{\frac{a}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a \cdot 2}\\ \end{array} \end{array} \]

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) (* (* z 9.0) t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+253)))
     (fma -4.5 (* z (/ t a)) (* 0.5 (/ y (/ a x))))
     (/ 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) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+253)) {
		tmp = fma(-4.5, (z * (t / a)), (0.5 * (y / (a / x))));
	} 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(Float64(z * 9.0) * t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+253))
		tmp = fma(-4.5, Float64(z * Float64(t / a)), Float64(0.5 * Float64(y / Float64(a / x))));
	else
		tmp = Float64(t_1 / Float64(a * 2.0));
	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[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+253]], $MachinePrecision]], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $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 4.9999999999999997e253 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 71.0%

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

      1. sub-neg 71.0%

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

      2. +-commutative 71.0%

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

      3. neg-sub0 71.0%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 71.0%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 71.0%

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

      6. neg-mul-1 71.0%

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

      7. associate-/l* 71.0%

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

      8. associate-/r/ 71.0%

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

      9. *-commutative 71.0%

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

      10. sub-neg 71.0%

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

      11. +-commutative 71.0%

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

      12. neg-sub0 71.0%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 71.0%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 71.0%

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

      15. distribute-lft-neg-out 71.0%

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

      16. distribute-rgt-neg-in 71.0%

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

   3. Simplified 73.7%

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

      1. *-commutative 73.7%

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

      2. metadata-eval 73.7%

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

      3. distribute-lft-neg-in 73.7%

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

      4. distribute-rgt-neg-in 73.7%

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

      5. fma-neg 72.3%

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

      6. associate-*r* 71.0%

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

      7. *-commutative 71.0%

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

   5. Applied egg-rr 71.0%

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

   6. Taylor expanded in x around 0 69.5%

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

      1. fma-def 69.5%

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

      2. *-commutative 69.5%

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

      3. associate-*r/ 77.2%

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

      4. associate-/l* 92.9%

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

   8. Simplified 92.9%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 4.9999999999999997e253

   1. Initial program 98.4%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+253}\right):\\ \;\;\;\;\mathsf{fma}\left(-4.5, z \cdot \frac{t}{a}, 0.5 \cdot \frac{y}{\frac{a}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \end{array} \]

Alternative 2: 95.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+303} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+246}\right):\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{0.5}{a}\\ \end{array} \end{array} \]

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 (or (<= (* x y) -1e+303) (not (<= (* x y) 5e+246)))
   (* 0.5 (/ y (/ a x)))
   (* (- (* x y) (* (* z 9.0) t)) (/ 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 (((x * y) <= -1e+303) || !((x * y) <= 5e+246)) {
		tmp = 0.5 * (y / (a / x));
	} else {
		tmp = ((x * y) - ((z * 9.0) * t)) * (0.5 / 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 (((x * y) <= (-1d+303)) .or. (.not. ((x * y) <= 5d+246))) then
        tmp = 0.5d0 * (y / (a / x))
    else
        tmp = ((x * y) - ((z * 9.0d0) * t)) * (0.5d0 / 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 (((x * y) <= -1e+303) || !((x * y) <= 5e+246)) {
		tmp = 0.5 * (y / (a / x));
	} else {
		tmp = ((x * y) - ((z * 9.0) * t)) * (0.5 / 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) <= -1e+303) or not ((x * y) <= 5e+246):
		tmp = 0.5 * (y / (a / x))
	else:
		tmp = ((x * y) - ((z * 9.0) * t)) * (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(x * y) <= -1e+303) || !(Float64(x * y) <= 5e+246))
		tmp = Float64(0.5 * Float64(y / Float64(a / x)));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) * Float64(0.5 / 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) <= -1e+303) || ~(((x * y) <= 5e+246)))
		tmp = 0.5 * (y / (a / x));
	else
		tmp = ((x * y) - ((z * 9.0) * t)) * (0.5 / 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[Or[LessEqual[N[(x * y), $MachinePrecision], -1e+303], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e+246]], $MachinePrecision]], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1e303 or 4.99999999999999976e246 < (*.f64 x y)

   1. Initial program 67.3%

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

      1. sub-neg 67.3%

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

      2. +-commutative 67.3%

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

      3. neg-sub0 67.3%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 67.3%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 67.3%

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

      6. neg-mul-1 67.3%

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

      7. associate-/l* 67.3%

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

      8. associate-/r/ 67.1%

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

      9. *-commutative 67.1%

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

      10. sub-neg 67.1%

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

      11. +-commutative 67.1%

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

      12. neg-sub0 67.1%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 67.1%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 67.1%

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

      15. distribute-lft-neg-out 67.1%

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

      16. distribute-rgt-neg-in 67.1%

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

   3. Simplified 69.6%

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

      1. *-commutative 69.6%

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

      2. metadata-eval 69.6%

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

      3. distribute-lft-neg-in 69.6%

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

      4. distribute-rgt-neg-in 69.6%

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

      5. fma-neg 67.1%

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

      6. associate-*r* 67.1%

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

      7. *-commutative 67.1%

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

   5. Applied egg-rr 67.1%

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

   6. Taylor expanded in x around inf 69.8%

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

      1. associate-/l* 93.1%

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

   8. Simplified 93.1%

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

   if -1e303 < (*.f64 x y) < 4.99999999999999976e246

   1. Initial program 95.1%

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

      1. sub-neg 95.1%

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

      2. +-commutative 95.1%

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

      3. neg-sub0 95.1%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 95.1%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 95.1%

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

      6. neg-mul-1 95.1%

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

      7. associate-/l* 95.0%

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

      8. associate-/r/ 95.0%

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

      9. *-commutative 95.0%

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

      10. sub-neg 95.0%

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

      11. +-commutative 95.0%

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

      12. neg-sub0 95.0%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 95.0%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 95.0%

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

      15. distribute-lft-neg-out 95.0%

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

      16. distribute-rgt-neg-in 95.0%

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

   3. Simplified 95.5%

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

      1. *-commutative 95.5%

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

      2. metadata-eval 95.5%

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

      3. distribute-lft-neg-in 95.5%

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

      4. distribute-rgt-neg-in 95.5%

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

      5. fma-neg 95.5%

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

      6. associate-*r* 95.0%

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

      7. *-commutative 95.0%

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

   5. Applied egg-rr 95.0%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+303} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+246}\right):\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{0.5}{a}\\ \end{array} \]

Alternative 3: 95.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+252}\right):\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \end{array} \end{array} \]

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
 (if (or (<= (* x y) (- INFINITY)) (not (<= (* x y) 2e+252)))
   (* 0.5 (/ y (/ a x)))
   (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0))))

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)) || !((x * y) <= 2e+252)) {
		tmp = 0.5 * (y / (a / x));
	} else {
		tmp = ((x * y) - ((z * 9.0) * t)) / (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 tmp;
	if (((x * y) <= -Double.POSITIVE_INFINITY) || !((x * y) <= 2e+252)) {
		tmp = 0.5 * (y / (a / x));
	} else {
		tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
	}
	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) or not ((x * y) <= 2e+252):
		tmp = 0.5 * (y / (a / x))
	else:
		tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0)
	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)) || !(Float64(x * y) <= 2e+252))
		tmp = Float64(0.5 * Float64(y / Float64(a / x)));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / 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)
	tmp = 0.0;
	if (((x * y) <= -Inf) || ~(((x * y) <= 2e+252)))
		tmp = 0.5 * (y / (a / x));
	else
		tmp = ((x * y) - ((z * 9.0) * t)) / (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_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2e+252]], $MachinePrecision]], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -inf.0 or 2.0000000000000002e252 < (*.f64 x y)

   1. Initial program 64.7%

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

      1. sub-neg 64.7%

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

      2. +-commutative 64.7%

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

      3. neg-sub0 64.7%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 64.7%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 64.7%

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

      6. neg-mul-1 64.7%

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

      7. associate-/l* 64.8%

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

      8. associate-/r/ 64.7%

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

      9. *-commutative 64.7%

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

      10. sub-neg 64.7%

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

      11. +-commutative 64.7%

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

      12. neg-sub0 64.7%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 64.7%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 64.7%

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

      15. distribute-lft-neg-out 64.7%

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

      16. distribute-rgt-neg-in 64.7%

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

   3. Simplified 67.3%

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

      1. *-commutative 67.3%

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

      2. metadata-eval 67.3%

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

      3. distribute-lft-neg-in 67.3%

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

      4. distribute-rgt-neg-in 67.3%

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

      5. fma-neg 64.7%

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

      6. associate-*r* 64.7%

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

      7. *-commutative 64.7%

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

   5. Applied egg-rr 64.7%

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

   6. Taylor expanded in x around inf 67.4%

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

      1. associate-/l* 92.6%

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

   8. Simplified 92.6%

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

   if -inf.0 < (*.f64 x y) < 2.0000000000000002e252

   1. Initial program 95.2%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+252}\right):\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \end{array} \]

Alternative 4: 67.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{-41} \lor \neg \left(t \leq 2.15 \cdot 10^{+110}\right):\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

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 (or (<= t -8.6e-41) (not (<= t 2.15e+110)))
   (* -4.5 (* z (/ t a)))
   (* 0.5 (/ y (/ a x)))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.6e-41) || !(t <= 2.15e+110)) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = 0.5 * (y / (a / x));
	}
	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 ((t <= (-8.6d-41)) .or. (.not. (t <= 2.15d+110))) then
        tmp = (-4.5d0) * (z * (t / a))
    else
        tmp = 0.5d0 * (y / (a / x))
    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 ((t <= -8.6e-41) || !(t <= 2.15e+110)) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = 0.5 * (y / (a / x));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8.6e-41) or not (t <= 2.15e+110):
		tmp = -4.5 * (z * (t / a))
	else:
		tmp = 0.5 * (y / (a / x))
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8.6e-41) || !(t <= 2.15e+110))
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	else
		tmp = Float64(0.5 * Float64(y / Float64(a / x)));
	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 ((t <= -8.6e-41) || ~((t <= 2.15e+110)))
		tmp = -4.5 * (z * (t / a));
	else
		tmp = 0.5 * (y / (a / x));
	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[Or[LessEqual[t, -8.6e-41], N[Not[LessEqual[t, 2.15e+110]], $MachinePrecision]], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.5999999999999997e-41 or 2.15000000000000003e110 < t

   1. Initial program 88.6%

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

      1. div-sub 85.1%

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

      2. +-rgt-identity 85.1%

         \[\leadsto \frac{\color{blue}{x \cdot y + 0}}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

      3. div-sub 88.6%

         \[\leadsto \color{blue}{\frac{\left(x \cdot y + 0\right) - \left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

      4. +-rgt-identity 88.6%

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

      5. fma-neg 89.5%

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

      6. associate-*l* 89.6%

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

      7. distribute-rgt-neg-in 89.6%

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

      8. *-commutative 89.6%

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

      9. distribute-rgt-neg-in 89.6%

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

      10. metadata-eval 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in x around 0 68.8%

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

      1. associate-/l* 70.5%

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

      2. associate-/r/ 72.0%

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

   6. Simplified 72.0%

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

   if -8.5999999999999997e-41 < t < 2.15000000000000003e110

   1. Initial program 92.2%

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

      1. sub-neg 92.2%

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

      2. +-commutative 92.2%

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

      3. neg-sub0 92.2%

         \[\leadsto \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]

      4. associate-+l- 92.2%

         \[\leadsto \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]

      5. sub0-neg 92.2%

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

      6. neg-mul-1 92.2%

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

      7. associate-/l* 92.1%

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

      8. associate-/r/ 92.1%

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

      9. *-commutative 92.1%

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

      10. sub-neg 92.1%

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

      11. +-commutative 92.1%

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

      12. neg-sub0 92.1%

          \[\leadsto \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]

      13. associate-+l- 92.1%

          \[\leadsto \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]

      14. sub0-neg 92.1%

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

      15. distribute-lft-neg-out 92.1%

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

      16. distribute-rgt-neg-in 92.1%

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

   3. Simplified 92.8%

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

      1. *-commutative 92.8%

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

      2. metadata-eval 92.8%

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

      3. distribute-lft-neg-in 92.8%

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

      4. distribute-rgt-neg-in 92.8%

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

      5. fma-neg 92.8%

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

      6. associate-*r* 92.1%

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

      7. *-commutative 92.1%

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

   5. Applied egg-rr 92.1%

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

   6. Taylor expanded in x around inf 67.1%

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

      1. associate-/l* 65.2%

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

   8. Simplified 65.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{\frac{a}{x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{-41} \lor \neg \left(t \leq 2.15 \cdot 10^{+110}\right):\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \end{array} \]

Alternative 5: 67.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-48} \lor \neg \left(t \leq 2.25 \cdot 10^{+110}\right):\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{\frac{a}{x}}\\ \end{array} \end{array} \]

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 (or (<= t -6e-48) (not (<= t 2.25e+110)))
   (* -4.5 (* z (/ t a)))
   (/ (* y 0.5) (/ a x))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6e-48) || !(t <= 2.25e+110)) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = (y * 0.5) / (a / x);
	}
	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 ((t <= (-6d-48)) .or. (.not. (t <= 2.25d+110))) then
        tmp = (-4.5d0) * (z * (t / a))
    else
        tmp = (y * 0.5d0) / (a / x)
    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 ((t <= -6e-48) || !(t <= 2.25e+110)) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = (y * 0.5) / (a / x);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6e-48) or not (t <= 2.25e+110):
		tmp = -4.5 * (z * (t / a))
	else:
		tmp = (y * 0.5) / (a / x)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6e-48) || !(t <= 2.25e+110))
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	else
		tmp = Float64(Float64(y * 0.5) / Float64(a / x));
	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 ((t <= -6e-48) || ~((t <= 2.25e+110)))
		tmp = -4.5 * (z * (t / a));
	else
		tmp = (y * 0.5) / (a / x);
	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[Or[LessEqual[t, -6e-48], N[Not[LessEqual[t, 2.25e+110]], $MachinePrecision]], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 0.5), $MachinePrecision] / N[(a / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.9999999999999998e-48 or 2.2500000000000001e110 < t

   1. Initial program 88.8%

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

      1. div-sub 85.3%

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

      2. +-rgt-identity 85.3%

         \[\leadsto \frac{\color{blue}{x \cdot y + 0}}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

      3. div-sub 88.8%

         \[\leadsto \color{blue}{\frac{\left(x \cdot y + 0\right) - \left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

      4. +-rgt-identity 88.8%

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

      5. fma-neg 89.7%

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

      6. associate-*l* 89.8%

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

      7. distribute-rgt-neg-in 89.8%

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

      8. *-commutative 89.8%

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

      9. distribute-rgt-neg-in 89.8%

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

      10. metadata-eval 89.8%

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

   3. Simplified 89.8%

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

   4. Taylor expanded in x around 0 67.6%

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

      1. associate-/l* 69.3%

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

      2. associate-/r/ 70.8%

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

   6. Simplified 70.8%

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

   if -5.9999999999999998e-48 < t < 2.2500000000000001e110

   1. Initial program 92.1%

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

      1. sub-neg 92.1%

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

      2. +-commutative 92.1%

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

      3. associate-*l* 92.8%

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

      4. distribute-rgt-neg-in 92.8%

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

      5. fma-def 92.8%

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

      6. *-commutative 92.8%

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

      7. distribute-rgt-neg-in 92.8%

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

      8. metadata-eval 92.8%

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

   3. Simplified 92.8%

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

      1. add-cube-cbrt 91.4%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{\mathsf{fma}\left(z, t \cdot -9, x \cdot y\right)} \cdot \sqrt[3]{\mathsf{fma}\left(z, t \cdot -9, x \cdot y\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(z, t \cdot -9, x \cdot y\right)}}}{a \cdot 2} \]

      2. pow3 91.3%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(z, t \cdot -9, x \cdot y\right)}\right)}^{3}}}{a \cdot 2} \]

   5. Applied egg-rr 91.3%

      \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(z, t \cdot -9, x \cdot y\right)}\right)}^{3}}}{a \cdot 2} \]

   6. Taylor expanded in z around 0 66.6%

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

      1. associate-/l* 64.7%

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

      2. associate-*r/ 64.8%

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

      3. associate-/r/ 69.5%

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

      4. *-commutative 69.5%

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

   8. Simplified 69.5%

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

      1. div-inv 69.4%

         \[\leadsto \color{blue}{\left(\left(y \cdot 0.5\right) \cdot \frac{1}{a}\right)} \cdot x \]

      2. associate-*r* 65.2%

         \[\leadsto \color{blue}{\left(y \cdot 0.5\right) \cdot \left(\frac{1}{a} \cdot x\right)} \]

      3. associate-/r/ 64.1%

         \[\leadsto \left(y \cdot 0.5\right) \cdot \color{blue}{\frac{1}{\frac{a}{x}}} \]

      4. un-div-inv 64.8%

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

   10. Applied egg-rr 64.8%

       \[\leadsto \color{blue}{\frac{y \cdot 0.5}{\frac{a}{x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-48} \lor \neg \left(t \leq 2.25 \cdot 10^{+110}\right):\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{\frac{a}{x}}\\ \end{array} \]

Alternative 6: 51.5% 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 90.7%

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

   1. div-sub 89.1%

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

   2. +-rgt-identity 89.1%

      \[\leadsto \frac{\color{blue}{x \cdot y + 0}}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

   3. div-sub 90.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot y + 0\right) - \left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

   4. +-rgt-identity 90.7%

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

   5. fma-neg 91.1%

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

   6. associate-*l* 91.4%

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

   7. distribute-rgt-neg-in 91.4%

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

   8. *-commutative 91.4%

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

   9. distribute-rgt-neg-in 91.4%

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

   10. metadata-eval 91.4%

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

3. Simplified 91.4%

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

4. Taylor expanded in x around 0 48.8%

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

   1. associate-/l* 50.2%

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

   2. associate-/r/ 49.0%

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

6. Simplified 49.0%

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

7. Final simplification 49.0%

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

Alternative 7: 51.7% 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 90.7%

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

   1. div-sub 89.1%

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

   2. +-rgt-identity 89.1%

      \[\leadsto \frac{\color{blue}{x \cdot y + 0}}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

   3. div-sub 90.7%

      \[\leadsto \color{blue}{\frac{\left(x \cdot y + 0\right) - \left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]

   4. +-rgt-identity 90.7%

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

   5. fma-neg 91.1%

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

   6. associate-*l* 91.4%

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

   7. distribute-rgt-neg-in 91.4%

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

   8. *-commutative 91.4%

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

   9. distribute-rgt-neg-in 91.4%

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

   10. metadata-eval 91.4%

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

3. Simplified 91.4%

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

4. Taylor expanded in x around 0 48.8%

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

   1. associate-/l* 50.2%

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

6. Simplified 50.2%

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

7. Final simplification 50.2%

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

Developer target: 93.5% 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 2023223 
(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)))