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

Percentage Accurate: 91.3% → 96.0%

Time: 8.9s

Alternatives: 9

Speedup: 0.5×

• 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: 91.3% 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: 96.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 2 \cdot 10^{+303}\right):\\ \;\;\;\;y \cdot \mathsf{fma}\left(-4.5, \frac{z \cdot \frac{t}{y}}{a}, \frac{x \cdot 0.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(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 2e+303)))
     (* y (fma -4.5 (/ (* z (/ t y)) a) (/ (* x 0.5) a)))
     (/ t_1 (* a 2.0)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+303)) {
		tmp = y * fma(-4.5, ((z * (t / y)) / a), ((x * 0.5) / a));
	} else {
		tmp = t_1 / (a * 2.0);
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+303))
		tmp = Float64(y * fma(-4.5, Float64(Float64(z * Float64(t / y)) / a), Float64(Float64(x * 0.5) / a)));
	else
		tmp = Float64(t_1 / Float64(a * 2.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+303]], $MachinePrecision]], N[(y * N[(-4.5 * N[(N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] + N[(N[(x * 0.5), $MachinePrecision] / 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 #s(literal 9 binary64)) t)) < -inf.0 or 2e303 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 64.5%

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

   3. Taylor expanded in y around inf 78.3%

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

      1. fma-define 78.3%

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

      2. *-commutative 78.3%

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

      3. associate-/r* 78.6%

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

      4. *-commutative 78.6%

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

      5. associate-/l* 90.0%

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

      6. associate-*r/ 90.0%

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

   5. Simplified 90.0%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 2e303

   1. Initial program 99.1%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+303}\right):\\ \;\;\;\;y \cdot \mathsf{fma}\left(-4.5, \frac{z \cdot \frac{t}{y}}{a}, \frac{x \cdot 0.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 72.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+37} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{-135} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{-90}\right) \land x \cdot y \leq 5 \cdot 10^{+112}\right):\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* x y) -1e+37)
         (not
          (or (<= (* x y) 5e-135)
              (and (not (<= (* x y) 5e-90)) (<= (* x y) 5e+112)))))
   (* 0.5 (* y (/ x a)))
   (* -4.5 (/ (* z t) a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -1e+37) || !(((x * y) <= 5e-135) || (!((x * y) <= 5e-90) && ((x * y) <= 5e+112)))) {
		tmp = 0.5 * (y * (x / a));
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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+37)) .or. (.not. ((x * y) <= 5d-135) .or. (.not. ((x * y) <= 5d-90)) .and. ((x * y) <= 5d+112))) then
        tmp = 0.5d0 * (y * (x / a))
    else
        tmp = (-4.5d0) * ((z * t) / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -1e+37) || !(((x * y) <= 5e-135) || (!((x * y) <= 5e-90) && ((x * y) <= 5e+112)))) {
		tmp = 0.5 * (y * (x / a));
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if ((x * y) <= -1e+37) or not (((x * y) <= 5e-135) or (not ((x * y) <= 5e-90) and ((x * y) <= 5e+112))):
		tmp = 0.5 * (y * (x / a))
	else:
		tmp = -4.5 * ((z * t) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(x * y) <= -1e+37) || !((Float64(x * y) <= 5e-135) || (!(Float64(x * y) <= 5e-90) && (Float64(x * y) <= 5e+112))))
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	else
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x * y) <= -1e+37) || ~((((x * y) <= 5e-135) || (~(((x * y) <= 5e-90)) && ((x * y) <= 5e+112)))))
		tmp = 0.5 * (y * (x / a));
	else
		tmp = -4.5 * ((z * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -1e+37], N[Not[Or[LessEqual[N[(x * y), $MachinePrecision], 5e-135], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e-90]], $MachinePrecision], LessEqual[N[(x * y), $MachinePrecision], 5e+112]]]], $MachinePrecision]], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -9.99999999999999954e36 or 5.0000000000000002e-135 < (*.f64 x y) < 5.00000000000000019e-90 or 5e112 < (*.f64 x y)

   1. Initial program 83.6%

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

      1. clear-num 83.5%

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

      2. inv-pow 83.5%

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

      3. *-commutative 83.5%

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

      4. associate-/l* 83.5%

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

      5. fma-neg 84.4%

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

      6. *-commutative 84.4%

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

      7. distribute-rgt-neg-in 84.4%

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

      8. distribute-rgt-neg-in 84.4%

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

      9. metadata-eval 84.4%

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

   4. Applied egg-rr 84.4%

      \[\leadsto \color{blue}{{\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 84.4%

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

      2. associate-/r* 84.4%

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

      3. metadata-eval 84.4%

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

      4. associate-*r* 84.4%

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

      5. *-commutative 84.4%

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

      6. metadata-eval 84.4%

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

      7. distribute-lft-neg-in 84.4%

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

      8. distribute-lft-neg-in 84.4%

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

      9. metadata-eval 84.4%

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

      10. associate-*r* 83.5%

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

      11. *-commutative 83.5%

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

      12. *-commutative 83.5%

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

   6. Simplified 83.5%

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

   7. Taylor expanded in x around inf 74.5%

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

      1. *-commutative 74.5%

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

      2. associate-*r/ 81.0%

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

   9. Simplified 81.0%

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

   if -9.99999999999999954e36 < (*.f64 x y) < 5.0000000000000002e-135 or 5.00000000000000019e-90 < (*.f64 x y) < 5e112

   1. Initial program 94.6%

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

   3. Taylor expanded in x around 0 76.2%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+37} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{-135} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{-90}\right) \land x \cdot y \leq 5 \cdot 10^{+112}\right):\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := 0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-135}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-90} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+112}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 0.5 (* y (/ x a)))))
   (if (<= (* x y) -1e+37)
     t_1
     (if (<= (* x y) 5e-135)
       (/ (* t (* z -4.5)) a)
       (if (or (<= (* x y) 5e-90) (not (<= (* x y) 5e+112)))
         t_1
         (* -4.5 (/ (* z t) a)))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (y * (x / a));
	double tmp;
	if ((x * y) <= -1e+37) {
		tmp = t_1;
	} else if ((x * y) <= 5e-135) {
		tmp = (t * (z * -4.5)) / a;
	} else if (((x * y) <= 5e-90) || !((x * y) <= 5e+112)) {
		tmp = t_1;
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 * (x / a))
    if ((x * y) <= (-1d+37)) then
        tmp = t_1
    else if ((x * y) <= 5d-135) then
        tmp = (t * (z * (-4.5d0))) / a
    else if (((x * y) <= 5d-90) .or. (.not. ((x * y) <= 5d+112))) then
        tmp = t_1
    else
        tmp = (-4.5d0) * ((z * t) / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (y * (x / a));
	double tmp;
	if ((x * y) <= -1e+37) {
		tmp = t_1;
	} else if ((x * y) <= 5e-135) {
		tmp = (t * (z * -4.5)) / a;
	} else if (((x * y) <= 5e-90) || !((x * y) <= 5e+112)) {
		tmp = t_1;
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = 0.5 * (y * (x / a))
	tmp = 0
	if (x * y) <= -1e+37:
		tmp = t_1
	elif (x * y) <= 5e-135:
		tmp = (t * (z * -4.5)) / a
	elif ((x * y) <= 5e-90) or not ((x * y) <= 5e+112):
		tmp = t_1
	else:
		tmp = -4.5 * ((z * t) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(0.5 * Float64(y * Float64(x / a)))
	tmp = 0.0
	if (Float64(x * y) <= -1e+37)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-135)
		tmp = Float64(Float64(t * Float64(z * -4.5)) / a);
	elseif ((Float64(x * y) <= 5e-90) || !(Float64(x * y) <= 5e+112))
		tmp = t_1;
	else
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = 0.5 * (y * (x / a));
	tmp = 0.0;
	if ((x * y) <= -1e+37)
		tmp = t_1;
	elseif ((x * y) <= 5e-135)
		tmp = (t * (z * -4.5)) / a;
	elseif (((x * y) <= 5e-90) || ~(((x * y) <= 5e+112)))
		tmp = t_1;
	else
		tmp = -4.5 * ((z * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+37], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-135], N[(N[(t * N[(z * -4.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[Or[LessEqual[N[(x * y), $MachinePrecision], 5e-90], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e+112]], $MachinePrecision]], t$95$1, N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.99999999999999954e36 or 5.0000000000000002e-135 < (*.f64 x y) < 5.00000000000000019e-90 or 5e112 < (*.f64 x y)

   1. Initial program 83.6%

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

      1. clear-num 83.5%

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

      2. inv-pow 83.5%

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

      3. *-commutative 83.5%

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

      4. associate-/l* 83.5%

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

      5. fma-neg 84.4%

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

      6. *-commutative 84.4%

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

      7. distribute-rgt-neg-in 84.4%

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

      8. distribute-rgt-neg-in 84.4%

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

      9. metadata-eval 84.4%

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

   4. Applied egg-rr 84.4%

      \[\leadsto \color{blue}{{\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 84.4%

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

      2. associate-/r* 84.4%

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

      3. metadata-eval 84.4%

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

      4. associate-*r* 84.4%

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

      5. *-commutative 84.4%

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

      6. metadata-eval 84.4%

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

      7. distribute-lft-neg-in 84.4%

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

      8. distribute-lft-neg-in 84.4%

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

      9. metadata-eval 84.4%

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

      10. associate-*r* 83.5%

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

      11. *-commutative 83.5%

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

      12. *-commutative 83.5%

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

   6. Simplified 83.5%

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

   7. Taylor expanded in x around inf 74.5%

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

      1. *-commutative 74.5%

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

      2. associate-*r/ 81.0%

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

   9. Simplified 81.0%

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

   if -9.99999999999999954e36 < (*.f64 x y) < 5.0000000000000002e-135

   1. Initial program 93.9%

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

      1. clear-num 93.8%

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

      2. inv-pow 93.8%

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

      3. *-commutative 93.8%

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

      4. associate-/l* 93.8%

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

      5. fma-neg 93.8%

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

      6. *-commutative 93.8%

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

      7. distribute-rgt-neg-in 93.8%

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

      8. distribute-rgt-neg-in 93.8%

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

      9. metadata-eval 93.8%

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

   4. Applied egg-rr 93.8%

      \[\leadsto \color{blue}{{\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 93.8%

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

      2. associate-/r* 93.8%

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

      3. metadata-eval 93.8%

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

      4. associate-*r* 93.9%

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

      5. *-commutative 93.9%

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

      6. metadata-eval 93.9%

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

      7. distribute-lft-neg-in 93.9%

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

      8. distribute-lft-neg-in 93.9%

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

      9. metadata-eval 93.9%

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

      10. associate-*r* 93.8%

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

      11. *-commutative 93.8%

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

      12. *-commutative 93.8%

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

   6. Simplified 93.8%

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

   7. Taylor expanded in x around 0 79.4%

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

      1. associate-*r/ 79.3%

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

      2. associate-*r* 79.3%

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

      3. *-commutative 79.3%

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

      4. associate-*l* 79.4%

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

      5. associate-*r/ 79.4%

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

      6. *-commutative 79.4%

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

   9. Simplified 79.4%

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

       1. associate-*r/ 79.3%

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

   11. Applied egg-rr 79.3%

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

   if 5.00000000000000019e-90 < (*.f64 x y) < 5e112

   1. Initial program 96.9%

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

   3. Taylor expanded in x around 0 65.4%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+37}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-135}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-90} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+112}\right):\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := 0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-135}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \mathbf{elif}\;\neg \left(x \cdot y \leq 5 \cdot 10^{-90}\right) \land x \cdot y \leq 5 \cdot 10^{+112}:\\ \;\;\;\;\frac{\frac{z}{-0.2222222222222222}}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 0.5 (* y (/ x a)))))
   (if (<= (* x y) -1e+37)
     t_1
     (if (<= (* x y) 5e-135)
       (/ (* t (* z -4.5)) a)
       (if (and (not (<= (* x y) 5e-90)) (<= (* x y) 5e+112))
         (/ (/ z -0.2222222222222222) (/ a t))
         t_1)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (y * (x / a));
	double tmp;
	if ((x * y) <= -1e+37) {
		tmp = t_1;
	} else if ((x * y) <= 5e-135) {
		tmp = (t * (z * -4.5)) / a;
	} else if (!((x * y) <= 5e-90) && ((x * y) <= 5e+112)) {
		tmp = (z / -0.2222222222222222) / (a / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.5d0 * (y * (x / a))
    if ((x * y) <= (-1d+37)) then
        tmp = t_1
    else if ((x * y) <= 5d-135) then
        tmp = (t * (z * (-4.5d0))) / a
    else if ((.not. ((x * y) <= 5d-90)) .and. ((x * y) <= 5d+112)) then
        tmp = (z / (-0.2222222222222222d0)) / (a / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 0.5 * (y * (x / a));
	double tmp;
	if ((x * y) <= -1e+37) {
		tmp = t_1;
	} else if ((x * y) <= 5e-135) {
		tmp = (t * (z * -4.5)) / a;
	} else if (!((x * y) <= 5e-90) && ((x * y) <= 5e+112)) {
		tmp = (z / -0.2222222222222222) / (a / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = 0.5 * (y * (x / a))
	tmp = 0
	if (x * y) <= -1e+37:
		tmp = t_1
	elif (x * y) <= 5e-135:
		tmp = (t * (z * -4.5)) / a
	elif not ((x * y) <= 5e-90) and ((x * y) <= 5e+112):
		tmp = (z / -0.2222222222222222) / (a / t)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(0.5 * Float64(y * Float64(x / a)))
	tmp = 0.0
	if (Float64(x * y) <= -1e+37)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-135)
		tmp = Float64(Float64(t * Float64(z * -4.5)) / a);
	elseif (!(Float64(x * y) <= 5e-90) && (Float64(x * y) <= 5e+112))
		tmp = Float64(Float64(z / -0.2222222222222222) / Float64(a / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = 0.5 * (y * (x / a));
	tmp = 0.0;
	if ((x * y) <= -1e+37)
		tmp = t_1;
	elseif ((x * y) <= 5e-135)
		tmp = (t * (z * -4.5)) / a;
	elseif (~(((x * y) <= 5e-90)) && ((x * y) <= 5e+112))
		tmp = (z / -0.2222222222222222) / (a / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+37], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-135], N[(N[(t * N[(z * -4.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[And[N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e-90]], $MachinePrecision], LessEqual[N[(x * y), $MachinePrecision], 5e+112]], N[(N[(z / -0.2222222222222222), $MachinePrecision] / N[(a / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.99999999999999954e36 or 5.0000000000000002e-135 < (*.f64 x y) < 5.00000000000000019e-90 or 5e112 < (*.f64 x y)

   1. Initial program 83.6%

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

      1. clear-num 83.5%

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

      2. inv-pow 83.5%

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

      3. *-commutative 83.5%

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

      4. associate-/l* 83.5%

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

      5. fma-neg 84.4%

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

      6. *-commutative 84.4%

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

      7. distribute-rgt-neg-in 84.4%

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

      8. distribute-rgt-neg-in 84.4%

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

      9. metadata-eval 84.4%

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

   4. Applied egg-rr 84.4%

      \[\leadsto \color{blue}{{\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 84.4%

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

      2. associate-/r* 84.4%

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

      3. metadata-eval 84.4%

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

      4. associate-*r* 84.4%

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

      5. *-commutative 84.4%

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

      6. metadata-eval 84.4%

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

      7. distribute-lft-neg-in 84.4%

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

      8. distribute-lft-neg-in 84.4%

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

      9. metadata-eval 84.4%

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

      10. associate-*r* 83.5%

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

      11. *-commutative 83.5%

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

      12. *-commutative 83.5%

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

   6. Simplified 83.5%

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

   7. Taylor expanded in x around inf 74.5%

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

      1. *-commutative 74.5%

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

      2. associate-*r/ 81.0%

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

   9. Simplified 81.0%

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

   if -9.99999999999999954e36 < (*.f64 x y) < 5.0000000000000002e-135

   1. Initial program 93.9%

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

      1. clear-num 93.8%

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

      2. inv-pow 93.8%

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

      3. *-commutative 93.8%

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

      4. associate-/l* 93.8%

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

      5. fma-neg 93.8%

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

      6. *-commutative 93.8%

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

      7. distribute-rgt-neg-in 93.8%

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

      8. distribute-rgt-neg-in 93.8%

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

      9. metadata-eval 93.8%

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

   4. Applied egg-rr 93.8%

      \[\leadsto \color{blue}{{\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 93.8%

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

      2. associate-/r* 93.8%

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

      3. metadata-eval 93.8%

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

      4. associate-*r* 93.9%

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

      5. *-commutative 93.9%

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

      6. metadata-eval 93.9%

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

      7. distribute-lft-neg-in 93.9%

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

      8. distribute-lft-neg-in 93.9%

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

      9. metadata-eval 93.9%

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

      10. associate-*r* 93.8%

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

      11. *-commutative 93.8%

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

      12. *-commutative 93.8%

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

   6. Simplified 93.8%

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

   7. Taylor expanded in x around 0 79.4%

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

      1. associate-*r/ 79.3%

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

      2. associate-*r* 79.3%

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

      3. *-commutative 79.3%

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

      4. associate-*l* 79.4%

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

      5. associate-*r/ 79.4%

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

      6. *-commutative 79.4%

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

   9. Simplified 79.4%

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

       1. associate-*r/ 79.3%

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

   11. Applied egg-rr 79.3%

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

   if 5.00000000000000019e-90 < (*.f64 x y) < 5e112

   1. Initial program 96.9%

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

   3. Taylor expanded in x around 0 65.4%

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

      1. associate-*r/ 65.3%

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

      2. associate-*r* 65.4%

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

      3. associate-*l/ 59.9%

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

      4. associate-*r/ 59.9%

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

      5. *-commutative 59.9%

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

      6. associate-*r/ 59.9%

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

   5. Simplified 59.9%

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

      1. clear-num 59.8%

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

      2. un-div-inv 62.3%

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

      3. *-un-lft-identity 62.3%

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

      4. times-frac 62.4%

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

      5. metadata-eval 62.4%

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

   7. Applied egg-rr 62.4%

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

      1. associate-/r* 62.5%

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

   9. Simplified 62.5%

      \[\leadsto \color{blue}{\frac{\frac{z}{-0.2222222222222222}}{\frac{a}{t}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+37}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-135}:\\ \;\;\;\;\frac{t \cdot \left(z \cdot -4.5\right)}{a}\\ \mathbf{elif}\;\neg \left(x \cdot y \leq 5 \cdot 10^{-90}\right) \land x \cdot y \leq 5 \cdot 10^{+112}:\\ \;\;\;\;\frac{\frac{z}{-0.2222222222222222}}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+299}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+258}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y + -9 \cdot \left(z \cdot t\right)}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -2e+299)
   (* 0.5 (* y (/ x a)))
   (if (<= (* x y) 5e+258)
     (/ 0.5 (/ a (+ (* x y) (* -9.0 (* z t)))))
     (* 0.5 (* x (/ y a))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+299) {
		tmp = 0.5 * (y * (x / a));
	} else if ((x * y) <= 5e+258) {
		tmp = 0.5 / (a / ((x * y) + (-9.0 * (z * t))));
	} else {
		tmp = 0.5 * (x * (y / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-2d+299)) then
        tmp = 0.5d0 * (y * (x / a))
    else if ((x * y) <= 5d+258) then
        tmp = 0.5d0 / (a / ((x * y) + ((-9.0d0) * (z * t))))
    else
        tmp = 0.5d0 * (x * (y / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -2e+299) {
		tmp = 0.5 * (y * (x / a));
	} else if ((x * y) <= 5e+258) {
		tmp = 0.5 / (a / ((x * y) + (-9.0 * (z * t))));
	} else {
		tmp = 0.5 * (x * (y / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e+299:
		tmp = 0.5 * (y * (x / a))
	elif (x * y) <= 5e+258:
		tmp = 0.5 / (a / ((x * y) + (-9.0 * (z * t))))
	else:
		tmp = 0.5 * (x * (y / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -2e+299)
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	elseif (Float64(x * y) <= 5e+258)
		tmp = Float64(0.5 / Float64(a / Float64(Float64(x * y) + Float64(-9.0 * Float64(z * t)))));
	else
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -2e+299)
		tmp = 0.5 * (y * (x / a));
	elseif ((x * y) <= 5e+258)
		tmp = 0.5 / (a / ((x * y) + (-9.0 * (z * t))));
	else
		tmp = 0.5 * (x * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -2e+299], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+258], N[(0.5 / N[(a / N[(N[(x * y), $MachinePrecision] + N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -2.0000000000000001e299

   1. Initial program 64.0%

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

      1. clear-num 63.9%

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

      2. inv-pow 63.9%

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

      3. *-commutative 63.9%

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

      4. associate-/l* 63.9%

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

      5. fma-neg 63.9%

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

      6. *-commutative 63.9%

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

      7. distribute-rgt-neg-in 63.9%

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

      8. distribute-rgt-neg-in 63.9%

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

      9. metadata-eval 63.9%

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

   4. Applied egg-rr 63.9%

      \[\leadsto \color{blue}{{\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 63.9%

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

      2. associate-/r* 63.9%

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

      3. metadata-eval 63.9%

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

      4. associate-*r* 63.9%

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

      5. *-commutative 63.9%

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

      6. metadata-eval 63.9%

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

      7. distribute-lft-neg-in 63.9%

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

      8. distribute-lft-neg-in 63.9%

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

      9. metadata-eval 63.9%

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

      10. associate-*r* 63.9%

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

      11. *-commutative 63.9%

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

      12. *-commutative 63.9%

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

   6. Simplified 63.9%

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

   7. Taylor expanded in x around inf 68.8%

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

      1. *-commutative 68.8%

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

      2. associate-*r/ 96.2%

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

   9. Simplified 96.2%

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

   if -2.0000000000000001e299 < (*.f64 x y) < 5e258

   1. Initial program 94.9%

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

      1. clear-num 94.8%

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

      2. inv-pow 94.8%

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

      3. *-commutative 94.8%

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

      4. associate-/l* 94.8%

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

      5. fma-neg 94.8%

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

      6. *-commutative 94.8%

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

      7. distribute-rgt-neg-in 94.8%

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

      8. distribute-rgt-neg-in 94.8%

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

      9. metadata-eval 94.8%

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

   4. Applied egg-rr 94.8%

      \[\leadsto \color{blue}{{\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 94.8%

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

      2. associate-/r* 94.8%

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

      3. metadata-eval 94.8%

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

      4. associate-*r* 94.8%

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

      5. *-commutative 94.8%

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

      6. metadata-eval 94.8%

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

      7. distribute-lft-neg-in 94.8%

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

      8. distribute-lft-neg-in 94.8%

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

      9. metadata-eval 94.8%

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

      10. associate-*r* 94.3%

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

      11. *-commutative 94.3%

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

      12. *-commutative 94.3%

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

   6. Simplified 94.3%

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

   7. Taylor expanded in a around 0 94.8%

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

   if 5e258 < (*.f64 x y)

   1. Initial program 61.7%

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

   3. Taylor expanded in x around inf 62.0%

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

      1. associate-/l* 93.3%

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

   5. Simplified 93.3%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+299}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+258}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y + -9 \cdot \left(z \cdot t\right)}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 94.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+303}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+258}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -5e+303)
   (* 0.5 (* y (/ x a)))
   (if (<= (* x y) 5e+258)
     (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0))
     (* 0.5 (* x (/ y a))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+303) {
		tmp = 0.5 * (y * (x / a));
	} else if ((x * y) <= 5e+258) {
		tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
	} else {
		tmp = 0.5 * (x * (y / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-5d+303)) then
        tmp = 0.5d0 * (y * (x / a))
    else if ((x * y) <= 5d+258) then
        tmp = ((x * y) - ((z * 9.0d0) * t)) / (a * 2.0d0)
    else
        tmp = 0.5d0 * (x * (y / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+303) {
		tmp = 0.5 * (y * (x / a));
	} else if ((x * y) <= 5e+258) {
		tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
	} else {
		tmp = 0.5 * (x * (y / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -5e+303:
		tmp = 0.5 * (y * (x / a))
	elif (x * y) <= 5e+258:
		tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0)
	else:
		tmp = 0.5 * (x * (y / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -5e+303)
		tmp = Float64(0.5 * Float64(y * Float64(x / a)));
	elseif (Float64(x * y) <= 5e+258)
		tmp = Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0));
	else
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -5e+303)
		tmp = 0.5 * (y * (x / a));
	elseif ((x * y) <= 5e+258)
		tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
	else
		tmp = 0.5 * (x * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+303], N[(0.5 * N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+258], N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.9999999999999997e303

   1. Initial program 62.4%

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

      1. clear-num 62.4%

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

      2. inv-pow 62.4%

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

      3. *-commutative 62.4%

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

      4. associate-/l* 62.4%

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

      5. fma-neg 62.4%

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

      6. *-commutative 62.4%

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

      7. distribute-rgt-neg-in 62.4%

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

      8. distribute-rgt-neg-in 62.4%

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

      9. metadata-eval 62.4%

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

   4. Applied egg-rr 62.4%

      \[\leadsto \color{blue}{{\left(2 \cdot \frac{a}{\mathsf{fma}\left(x, y, t \cdot \left(z \cdot -9\right)\right)}\right)}^{-1}} \]
   5. Step-by-step derivation

      1. unpow-1 62.4%

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

      2. associate-/r* 62.4%

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

      3. metadata-eval 62.4%

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

      4. associate-*r* 62.4%

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

      5. *-commutative 62.4%

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

      6. metadata-eval 62.4%

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

      7. distribute-lft-neg-in 62.4%

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

      8. distribute-lft-neg-in 62.4%

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

      9. metadata-eval 62.4%

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

      10. associate-*r* 62.4%

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

      11. *-commutative 62.4%

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

      12. *-commutative 62.4%

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

   6. Simplified 62.4%

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

   7. Taylor expanded in x around inf 67.5%

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

      1. *-commutative 67.5%

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

      2. associate-*r/ 96.1%

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

   9. Simplified 96.1%

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

   if -4.9999999999999997e303 < (*.f64 x y) < 5e258

   1. Initial program 94.9%

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

   if 5e258 < (*.f64 x y)

   1. Initial program 61.7%

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

   3. Taylor expanded in x around inf 62.0%

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

      1. associate-/l* 93.3%

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

   5. Simplified 93.3%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+303}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+258}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-138} \lor \neg \left(y \leq 7.8 \cdot 10^{-14}\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.6e-138) (not (<= y 7.8e-14)))
   (* 0.5 (* x (/ y a)))
   (* -4.5 (/ (* z t) a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.6e-138) || !(y <= 7.8e-14)) {
		tmp = 0.5 * (x * (y / a));
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 <= (-2.6d-138)) .or. (.not. (y <= 7.8d-14))) then
        tmp = 0.5d0 * (x * (y / a))
    else
        tmp = (-4.5d0) * ((z * t) / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.6e-138) || !(y <= 7.8e-14)) {
		tmp = 0.5 * (x * (y / a));
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.6e-138) or not (y <= 7.8e-14):
		tmp = 0.5 * (x * (y / a))
	else:
		tmp = -4.5 * ((z * t) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.6e-138) || !(y <= 7.8e-14))
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	else
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.6e-138) || ~((y <= 7.8e-14)))
		tmp = 0.5 * (x * (y / a));
	else
		tmp = -4.5 * ((z * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.6e-138], N[Not[LessEqual[y, 7.8e-14]], $MachinePrecision]], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6e-138 or 7.7999999999999996e-14 < y

   1. Initial program 85.9%

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

   3. Taylor expanded in x around inf 56.5%

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

      1. associate-/l* 64.5%

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

   5. Simplified 64.5%

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

   if -2.6e-138 < y < 7.7999999999999996e-14

   1. Initial program 96.1%

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

   3. Taylor expanded in x around 0 73.1%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-138} \lor \neg \left(y \leq 7.8 \cdot 10^{-14}\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+181}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.5e+181) (* -4.5 (* t (/ z a))) (* -4.5 (/ (* z t) a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e+181) {
		tmp = -4.5 * (t * (z / a));
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.5d+181)) then
        tmp = (-4.5d0) * (t * (z / a))
    else
        tmp = (-4.5d0) * ((z * t) / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.5e+181) {
		tmp = -4.5 * (t * (z / a));
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.5e+181:
		tmp = -4.5 * (t * (z / a))
	else:
		tmp = -4.5 * ((z * t) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.5e+181)
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	else
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.5e+181)
		tmp = -4.5 * (t * (z / a));
	else
		tmp = -4.5 * ((z * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.5e+181], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5000000000000002e181

   1. Initial program 85.3%

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

   3. Taylor expanded in x around 0 63.3%

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

      1. associate-/l* 70.9%

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

   5. Simplified 70.9%

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

   if -2.5000000000000002e181 < z

   1. Initial program 90.6%

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

   3. Taylor expanded in x around 0 50.6%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+181}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.7% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.1%

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

3. Taylor expanded in x around 0 51.9%

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

   1. associate-/l* 53.2%

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

5. Simplified 53.2%

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

6. Final simplification 53.2%

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

Developer target: 93.4% accurate, 0.5× 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 2024073 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :alt
  (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)))