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

Percentage Accurate: 91.2% → 95.4%

Time: 9.3s

Alternatives: 12

Speedup: 0.6×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.2% 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: 95.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+276}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) (- INFINITY))
   (* 0.5 (* x (/ y a)))
   (if (<= (* x y) 5e+276)
     (/ (- (* x y) (* t (* z 9.0))) (* a 2.0))
     (* 0.5 (/ x (/ a y))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = 0.5 * (x * (y / a));
	} else if ((x * y) <= 5e+276) {
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = 0.5 * (x * (y / a));
	} else if ((x * y) <= 5e+276) {
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = 0.5 * (x * (y / a))
	elif (x * y) <= 5e+276:
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0)
	else:
		tmp = 0.5 * (x / (a / y))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	elseif (Float64(x * y) <= 5e+276)
		tmp = Float64(Float64(Float64(x * y) - Float64(t * Float64(z * 9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -Inf)
		tmp = 0.5 * (x * (y / a));
	elseif ((x * y) <= 5e+276)
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0);
	else
		tmp = 0.5 * (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+276], N[(N[(N[(x * y), $MachinePrecision] - N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 51.8%

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

   3. Taylor expanded in x around inf 66.4%

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

      1. associate-/l* 92.8%

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

   5. Simplified 92.8%

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

   if -inf.0 < (*.f64 x y) < 5.00000000000000001e276

   1. Initial program 97.5%

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

   if 5.00000000000000001e276 < (*.f64 x y)

   1. Initial program 66.4%

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

      1. *-un-lft-identity 66.4%

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

      2. *-un-lft-identity 66.4%

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

      3. fma-neg 66.4%

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

      4. distribute-lft-neg-in 66.4%

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

      5. distribute-rgt-neg-in 66.4%

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

      6. metadata-eval 66.4%

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

      7. associate-*r* 66.4%

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

      8. *-commutative 66.4%

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

      9. clear-num 66.4%

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

      10. inv-pow 66.4%

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

      11. associate-/l* 66.4%

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

   4. Applied egg-rr 66.4%

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

      1. unpow-1 66.4%

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

      2. fma-define 66.4%

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

      3. +-commutative 66.4%

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

      4. fma-define 66.4%

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

   6. Simplified 66.4%

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

   7. Taylor expanded in z around 0 66.4%

      \[\leadsto \frac{1}{\color{blue}{2 \cdot \frac{a}{x \cdot y}}} \]
   8. Step-by-step derivation

      1. associate-/r* 100.0%

         \[\leadsto \frac{1}{2 \cdot \color{blue}{\frac{\frac{a}{x}}{y}}} \]

   9. Simplified 100.0%

      \[\leadsto \frac{1}{\color{blue}{2 \cdot \frac{\frac{a}{x}}{y}}} \]
   10. Step-by-step derivation

       1. *-un-lft-identity 100.0%

          \[\leadsto \color{blue}{1 \cdot \frac{1}{2 \cdot \frac{\frac{a}{x}}{y}}} \]

       2. associate-/r* 100.0%

          \[\leadsto 1 \cdot \color{blue}{\frac{\frac{1}{2}}{\frac{\frac{a}{x}}{y}}} \]

       3. metadata-eval 100.0%

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

   11. Applied egg-rr 100.0%

       \[\leadsto \color{blue}{1 \cdot \frac{0.5}{\frac{\frac{a}{x}}{y}}} \]
   12. Step-by-step derivation

       1. *-lft-identity 100.0%

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

       2. associate-/r* 66.4%

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

   13. Simplified 66.4%

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

       1. div-inv 66.4%

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

       2. clear-num 66.4%

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

       3. *-commutative 66.4%

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

       4. associate-*r/ 99.9%

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

       5. clear-num 99.9%

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

       6. un-div-inv 99.9%

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

   15. Applied egg-rr 99.9%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+276}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 4 \cdot 10^{-31}:\\ \;\;\;\;\frac{1}{a \cdot \frac{2}{\mathsf{fma}\left(z, t \cdot -9, x \cdot y\right)}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2} - t \cdot \frac{z \cdot 9}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 2.0) 4e-31)
   (/ 1.0 (* a (/ 2.0 (fma z (* t -9.0) (* x y)))))
   (- (* y (/ x (* a 2.0))) (* t (/ (* z 9.0) (* a 2.0))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 2.0) <= 4e-31) {
		tmp = 1.0 / (a * (2.0 / fma(z, (t * -9.0), (x * y))));
	} else {
		tmp = (y * (x / (a * 2.0))) - (t * ((z * 9.0) / (a * 2.0)));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 2.0) <= 4e-31)
		tmp = Float64(1.0 / Float64(a * Float64(2.0 / fma(z, Float64(t * -9.0), Float64(x * y)))));
	else
		tmp = Float64(Float64(y * Float64(x / Float64(a * 2.0))) - Float64(t * Float64(Float64(z * 9.0) / 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.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 2.0), $MachinePrecision], 4e-31], N[(1.0 / N[(a * N[(2.0 / N[(z * N[(t * -9.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(x / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(z * 9.0), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 2 binary64)) < 4e-31

   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. *-un-lft-identity 94.9%

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

      2. *-un-lft-identity 94.9%

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

      3. fma-neg 95.0%

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

      4. distribute-lft-neg-in 95.0%

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

      5. distribute-rgt-neg-in 95.0%

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

      6. metadata-eval 95.0%

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

      7. associate-*r* 95.0%

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

      8. *-commutative 95.0%

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

      9. clear-num 94.4%

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

      10. inv-pow 94.4%

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

      11. associate-/l* 94.3%

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

   4. Applied egg-rr 94.3%

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

      1. unpow-1 94.3%

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

      2. fma-define 94.2%

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

      3. +-commutative 94.2%

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

      4. fma-define 95.3%

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

   6. Simplified 95.3%

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

   if 4e-31 < (*.f64 a #s(literal 2 binary64))

   1. Initial program 89.5%

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

      1. div-sub 89.5%

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

      2. *-commutative 89.5%

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

      3. associate-/l* 88.6%

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

      4. *-commutative 88.6%

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

      5. associate-/l* 89.8%

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

   4. Applied egg-rr 89.8%

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

Alternative 3: 74.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+91}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+25}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-80}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot 0.5\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+29}:\\ \;\;\;\;\frac{z \cdot \left(t \cdot -4.5\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -4e+91)
   (* 0.5 (* x (/ y a)))
   (if (<= (* x y) -5e+25)
     (* -4.5 (* t (/ z a)))
     (if (<= (* x y) -5e-80)
       (/ (* x (* y 0.5)) a)
       (if (<= (* x y) 1e+29) (/ (* z (* t -4.5)) a) (* (* y 0.5) (/ x a)))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e+91) {
		tmp = 0.5 * (x * (y / a));
	} else if ((x * y) <= -5e+25) {
		tmp = -4.5 * (t * (z / a));
	} else if ((x * y) <= -5e-80) {
		tmp = (x * (y * 0.5)) / a;
	} else if ((x * y) <= 1e+29) {
		tmp = (z * (t * -4.5)) / a;
	} else {
		tmp = (y * 0.5) * (x / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-4d+91)) then
        tmp = 0.5d0 * (x * (y / a))
    else if ((x * y) <= (-5d+25)) then
        tmp = (-4.5d0) * (t * (z / a))
    else if ((x * y) <= (-5d-80)) then
        tmp = (x * (y * 0.5d0)) / a
    else if ((x * y) <= 1d+29) then
        tmp = (z * (t * (-4.5d0))) / a
    else
        tmp = (y * 0.5d0) * (x / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e+91) {
		tmp = 0.5 * (x * (y / a));
	} else if ((x * y) <= -5e+25) {
		tmp = -4.5 * (t * (z / a));
	} else if ((x * y) <= -5e-80) {
		tmp = (x * (y * 0.5)) / a;
	} else if ((x * y) <= 1e+29) {
		tmp = (z * (t * -4.5)) / a;
	} else {
		tmp = (y * 0.5) * (x / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -4e+91:
		tmp = 0.5 * (x * (y / a))
	elif (x * y) <= -5e+25:
		tmp = -4.5 * (t * (z / a))
	elif (x * y) <= -5e-80:
		tmp = (x * (y * 0.5)) / a
	elif (x * y) <= 1e+29:
		tmp = (z * (t * -4.5)) / a
	else:
		tmp = (y * 0.5) * (x / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -4e+91)
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	elseif (Float64(x * y) <= -5e+25)
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	elseif (Float64(x * y) <= -5e-80)
		tmp = Float64(Float64(x * Float64(y * 0.5)) / a);
	elseif (Float64(x * y) <= 1e+29)
		tmp = Float64(Float64(z * Float64(t * -4.5)) / a);
	else
		tmp = Float64(Float64(y * 0.5) * Float64(x / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -4e+91)
		tmp = 0.5 * (x * (y / a));
	elseif ((x * y) <= -5e+25)
		tmp = -4.5 * (t * (z / a));
	elseif ((x * y) <= -5e-80)
		tmp = (x * (y * 0.5)) / a;
	elseif ((x * y) <= 1e+29)
		tmp = (z * (t * -4.5)) / a;
	else
		tmp = (y * 0.5) * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -4e+91], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5e+25], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5e-80], N[(N[(x * N[(y * 0.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+29], N[(N[(z * N[(t * -4.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(y * 0.5), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -4.00000000000000032e91

   1. Initial program 83.0%

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

   3. Taylor expanded in x around inf 76.5%

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

      1. associate-/l* 81.0%

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

   5. Simplified 81.0%

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

   if -4.00000000000000032e91 < (*.f64 x y) < -5.00000000000000024e25

   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 64.8%

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

      1. associate-*r/ 64.5%

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

      2. associate-*r* 64.5%

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

      3. associate-*l/ 73.4%

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

      4. associate-*r/ 73.4%

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

      5. associate-*l* 73.7%

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

   5. Simplified 73.7%

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

      1. associate-*l/ 64.8%

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

      2. *-commutative 64.8%

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

   7. Applied egg-rr 64.8%

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

   8. Taylor expanded in z around 0 64.8%

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

      1. associate-*r/ 56.3%

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

   10. Simplified 56.3%

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

   if -5.00000000000000024e25 < (*.f64 x y) < -5e-80

   1. Initial program 99.5%

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

      1. associate-/l/ 99.5%

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

      2. div-sub 99.5%

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

      3. associate-/l* 99.5%

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

      4. fma-neg 99.5%

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

      5. *-commutative 99.5%

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

      6. associate-/l* 99.5%

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

      7. distribute-rgt-neg-out 99.5%

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

      8. distribute-frac-neg 99.5%

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

      9. distribute-rgt-neg-in 99.5%

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

      10. associate-/l* 99.5%

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

      11. metadata-eval 99.5%

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

      12. metadata-eval 99.5%

          \[\leadsto \frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot \color{blue}{-4.5}\right)\right)}{a} \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot -4.5\right)\right)}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 71.1%

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

      1. *-commutative 71.1%

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

      2. associate-*r* 71.1%

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

      3. *-commutative 71.1%

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

   7. Simplified 71.1%

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

   if -5e-80 < (*.f64 x y) < 9.99999999999999914e28

   1. Initial program 96.5%

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

   3. Taylor expanded in x around 0 80.0%

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

      1. associate-*r/ 80.0%

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

      2. associate-*r* 80.0%

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

   5. Simplified 80.0%

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

   if 9.99999999999999914e28 < (*.f64 x y)

   1. Initial program 92.1%

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

   3. Taylor expanded in z around inf 84.2%

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

   4. Taylor expanded in z around 0 72.5%

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

      1. associate-*r/ 72.5%

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

      2. associate-*r* 72.5%

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

      3. associate-*l/ 74.9%

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

      4. associate-*r/ 74.9%

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

      5. *-commutative 74.9%

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

      6. associate-*r* 74.9%

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

   6. Simplified 74.9%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+91}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+25}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-80}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot 0.5\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+29}:\\ \;\;\;\;\frac{z \cdot \left(t \cdot -4.5\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+91}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+25}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-80}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot 0.5\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+29}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -4e+91)
   (* 0.5 (* x (/ y a)))
   (if (<= (* x y) -5e+25)
     (* -4.5 (* t (/ z a)))
     (if (<= (* x y) -5e-80)
       (/ (* x (* y 0.5)) a)
       (if (<= (* x y) 1e+29) (* -4.5 (/ (* z t) a)) (* (* y 0.5) (/ x a)))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e+91) {
		tmp = 0.5 * (x * (y / a));
	} else if ((x * y) <= -5e+25) {
		tmp = -4.5 * (t * (z / a));
	} else if ((x * y) <= -5e-80) {
		tmp = (x * (y * 0.5)) / a;
	} else if ((x * y) <= 1e+29) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = (y * 0.5) * (x / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-4d+91)) then
        tmp = 0.5d0 * (x * (y / a))
    else if ((x * y) <= (-5d+25)) then
        tmp = (-4.5d0) * (t * (z / a))
    else if ((x * y) <= (-5d-80)) then
        tmp = (x * (y * 0.5d0)) / a
    else if ((x * y) <= 1d+29) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = (y * 0.5d0) * (x / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e+91) {
		tmp = 0.5 * (x * (y / a));
	} else if ((x * y) <= -5e+25) {
		tmp = -4.5 * (t * (z / a));
	} else if ((x * y) <= -5e-80) {
		tmp = (x * (y * 0.5)) / a;
	} else if ((x * y) <= 1e+29) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = (y * 0.5) * (x / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -4e+91:
		tmp = 0.5 * (x * (y / a))
	elif (x * y) <= -5e+25:
		tmp = -4.5 * (t * (z / a))
	elif (x * y) <= -5e-80:
		tmp = (x * (y * 0.5)) / a
	elif (x * y) <= 1e+29:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = (y * 0.5) * (x / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -4e+91)
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	elseif (Float64(x * y) <= -5e+25)
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	elseif (Float64(x * y) <= -5e-80)
		tmp = Float64(Float64(x * Float64(y * 0.5)) / a);
	elseif (Float64(x * y) <= 1e+29)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = Float64(Float64(y * 0.5) * Float64(x / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -4e+91)
		tmp = 0.5 * (x * (y / a));
	elseif ((x * y) <= -5e+25)
		tmp = -4.5 * (t * (z / a));
	elseif ((x * y) <= -5e-80)
		tmp = (x * (y * 0.5)) / a;
	elseif ((x * y) <= 1e+29)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = (y * 0.5) * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -4e+91], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5e+25], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5e-80], N[(N[(x * N[(y * 0.5), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+29], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(y * 0.5), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -4.00000000000000032e91

   1. Initial program 83.0%

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

   3. Taylor expanded in x around inf 76.5%

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

      1. associate-/l* 81.0%

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

   5. Simplified 81.0%

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

   if -4.00000000000000032e91 < (*.f64 x y) < -5.00000000000000024e25

   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 64.8%

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

      1. associate-*r/ 64.5%

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

      2. associate-*r* 64.5%

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

      3. associate-*l/ 73.4%

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

      4. associate-*r/ 73.4%

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

      5. associate-*l* 73.7%

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

   5. Simplified 73.7%

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

      1. associate-*l/ 64.8%

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

      2. *-commutative 64.8%

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

   7. Applied egg-rr 64.8%

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

   8. Taylor expanded in z around 0 64.8%

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

      1. associate-*r/ 56.3%

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

   10. Simplified 56.3%

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

   if -5.00000000000000024e25 < (*.f64 x y) < -5e-80

   1. Initial program 99.5%

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

      1. associate-/l/ 99.5%

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

      2. div-sub 99.5%

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

      3. associate-/l* 99.5%

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

      4. fma-neg 99.5%

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

      5. *-commutative 99.5%

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

      6. associate-/l* 99.5%

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

      7. distribute-rgt-neg-out 99.5%

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

      8. distribute-frac-neg 99.5%

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

      9. distribute-rgt-neg-in 99.5%

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

      10. associate-/l* 99.5%

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

      11. metadata-eval 99.5%

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

      12. metadata-eval 99.5%

          \[\leadsto \frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot \color{blue}{-4.5}\right)\right)}{a} \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, \frac{y}{2}, t \cdot \left(z \cdot -4.5\right)\right)}{a}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 71.1%

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

      1. *-commutative 71.1%

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

      2. associate-*r* 71.1%

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

      3. *-commutative 71.1%

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

   7. Simplified 71.1%

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

   if -5e-80 < (*.f64 x y) < 9.99999999999999914e28

   1. Initial program 96.5%

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

   3. Taylor expanded in x around 0 80.0%

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

   if 9.99999999999999914e28 < (*.f64 x y)

   1. Initial program 92.1%

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

   3. Taylor expanded in z around inf 84.2%

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

   4. Taylor expanded in z around 0 72.5%

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

      1. associate-*r/ 72.5%

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

      2. associate-*r* 72.5%

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

      3. associate-*l/ 74.9%

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

      4. associate-*r/ 74.9%

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

      5. *-commutative 74.9%

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

      6. associate-*r* 74.9%

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

   6. Simplified 74.9%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+91}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+25}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-80}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot 0.5\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+29}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+91}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+25}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-80}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+29}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -4e+91)
   (* 0.5 (* x (/ y a)))
   (if (<= (* x y) -5e+25)
     (* -4.5 (* t (/ z a)))
     (if (<= (* x y) -5e-80)
       (* (* x y) (/ 0.5 a))
       (if (<= (* x y) 1e+29) (* -4.5 (/ (* z t) a)) (* (* y 0.5) (/ x a)))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e+91) {
		tmp = 0.5 * (x * (y / a));
	} else if ((x * y) <= -5e+25) {
		tmp = -4.5 * (t * (z / a));
	} else if ((x * y) <= -5e-80) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 1e+29) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = (y * 0.5) * (x / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-4d+91)) then
        tmp = 0.5d0 * (x * (y / a))
    else if ((x * y) <= (-5d+25)) then
        tmp = (-4.5d0) * (t * (z / a))
    else if ((x * y) <= (-5d-80)) then
        tmp = (x * y) * (0.5d0 / a)
    else if ((x * y) <= 1d+29) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = (y * 0.5d0) * (x / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -4e+91) {
		tmp = 0.5 * (x * (y / a));
	} else if ((x * y) <= -5e+25) {
		tmp = -4.5 * (t * (z / a));
	} else if ((x * y) <= -5e-80) {
		tmp = (x * y) * (0.5 / a);
	} else if ((x * y) <= 1e+29) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = (y * 0.5) * (x / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -4e+91:
		tmp = 0.5 * (x * (y / a))
	elif (x * y) <= -5e+25:
		tmp = -4.5 * (t * (z / a))
	elif (x * y) <= -5e-80:
		tmp = (x * y) * (0.5 / a)
	elif (x * y) <= 1e+29:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = (y * 0.5) * (x / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -4e+91)
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	elseif (Float64(x * y) <= -5e+25)
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	elseif (Float64(x * y) <= -5e-80)
		tmp = Float64(Float64(x * y) * Float64(0.5 / a));
	elseif (Float64(x * y) <= 1e+29)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = Float64(Float64(y * 0.5) * Float64(x / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -4e+91)
		tmp = 0.5 * (x * (y / a));
	elseif ((x * y) <= -5e+25)
		tmp = -4.5 * (t * (z / a));
	elseif ((x * y) <= -5e-80)
		tmp = (x * y) * (0.5 / a);
	elseif ((x * y) <= 1e+29)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = (y * 0.5) * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -4e+91], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5e+25], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5e-80], N[(N[(x * y), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+29], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(y * 0.5), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -4.00000000000000032e91

   1. Initial program 83.0%

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

   3. Taylor expanded in x around inf 76.5%

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

      1. associate-/l* 81.0%

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

   5. Simplified 81.0%

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

   if -4.00000000000000032e91 < (*.f64 x y) < -5.00000000000000024e25

   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 64.8%

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

      1. associate-*r/ 64.5%

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

      2. associate-*r* 64.5%

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

      3. associate-*l/ 73.4%

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

      4. associate-*r/ 73.4%

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

      5. associate-*l* 73.7%

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

   5. Simplified 73.7%

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

      1. associate-*l/ 64.8%

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

      2. *-commutative 64.8%

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

   7. Applied egg-rr 64.8%

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

   8. Taylor expanded in z around 0 64.8%

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

      1. associate-*r/ 56.3%

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

   10. Simplified 56.3%

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

   if -5.00000000000000024e25 < (*.f64 x y) < -5e-80

   1. Initial program 99.5%

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

      1. *-un-lft-identity 99.5%

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

      2. *-un-lft-identity 99.5%

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

      3. fma-neg 99.5%

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

      4. distribute-lft-neg-in 99.5%

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

      5. distribute-rgt-neg-in 99.5%

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

      6. metadata-eval 99.5%

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

      7. associate-*r* 99.4%

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

      8. *-commutative 99.4%

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

      9. clear-num 98.1%

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

      10. inv-pow 98.1%

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

      11. associate-/l* 98.1%

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

   4. Applied egg-rr 98.1%

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

      1. unpow-1 98.1%

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

      2. fma-define 98.1%

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

      3. +-commutative 98.1%

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

      4. fma-define 98.1%

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

   6. Simplified 98.1%

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

   7. Taylor expanded in z around 0 69.8%

      \[\leadsto \frac{1}{\color{blue}{2 \cdot \frac{a}{x \cdot y}}} \]
   8. Step-by-step derivation

      1. associate-/r* 60.7%

         \[\leadsto \frac{1}{2 \cdot \color{blue}{\frac{\frac{a}{x}}{y}}} \]

   9. Simplified 60.7%

      \[\leadsto \frac{1}{\color{blue}{2 \cdot \frac{\frac{a}{x}}{y}}} \]
   10. Step-by-step derivation

       1. *-un-lft-identity 60.7%

          \[\leadsto \color{blue}{1 \cdot \frac{1}{2 \cdot \frac{\frac{a}{x}}{y}}} \]

       2. associate-/r* 60.7%

          \[\leadsto 1 \cdot \color{blue}{\frac{\frac{1}{2}}{\frac{\frac{a}{x}}{y}}} \]

       3. metadata-eval 60.7%

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

   11. Applied egg-rr 60.7%

       \[\leadsto \color{blue}{1 \cdot \frac{0.5}{\frac{\frac{a}{x}}{y}}} \]
   12. Step-by-step derivation

       1. *-lft-identity 60.7%

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

       2. associate-/r* 69.8%

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

   13. Simplified 69.8%

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

       1. associate-/r/ 71.0%

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

   15. Applied egg-rr 71.0%

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

   if -5e-80 < (*.f64 x y) < 9.99999999999999914e28

   1. Initial program 96.5%

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

   3. Taylor expanded in x around 0 80.0%

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

   if 9.99999999999999914e28 < (*.f64 x y)

   1. Initial program 92.1%

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

   3. Taylor expanded in z around inf 84.2%

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

   4. Taylor expanded in z around 0 72.5%

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

      1. associate-*r/ 72.5%

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

      2. associate-*r* 72.5%

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

      3. associate-*l/ 74.9%

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

      4. associate-*r/ 74.9%

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

      5. *-commutative 74.9%

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

      6. associate-*r* 74.9%

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

   6. Simplified 74.9%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+91}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{+25}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-80}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{0.5}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+29}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ t_2 := -4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+62}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-119}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* y 0.5) (/ x a))) (t_2 (* -4.5 (* t (/ z a)))))
   (if (<= z -2.3e+62)
     t_2
     (if (<= z -1.25e-85)
       t_1
       (if (<= z -9.5e-119)
         (* -4.5 (/ (* z t) a))
         (if (<= z 6.2e-43) t_1 t_2))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * 0.5) * (x / a);
	double t_2 = -4.5 * (t * (z / a));
	double tmp;
	if (z <= -2.3e+62) {
		tmp = t_2;
	} else if (z <= -1.25e-85) {
		tmp = t_1;
	} else if (z <= -9.5e-119) {
		tmp = -4.5 * ((z * t) / a);
	} else if (z <= 6.2e-43) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * 0.5d0) * (x / a)
    t_2 = (-4.5d0) * (t * (z / a))
    if (z <= (-2.3d+62)) then
        tmp = t_2
    else if (z <= (-1.25d-85)) then
        tmp = t_1
    else if (z <= (-9.5d-119)) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if (z <= 6.2d-43) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * 0.5) * (x / a);
	double t_2 = -4.5 * (t * (z / a));
	double tmp;
	if (z <= -2.3e+62) {
		tmp = t_2;
	} else if (z <= -1.25e-85) {
		tmp = t_1;
	} else if (z <= -9.5e-119) {
		tmp = -4.5 * ((z * t) / a);
	} else if (z <= 6.2e-43) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (y * 0.5) * (x / a)
	t_2 = -4.5 * (t * (z / a))
	tmp = 0
	if z <= -2.3e+62:
		tmp = t_2
	elif z <= -1.25e-85:
		tmp = t_1
	elif z <= -9.5e-119:
		tmp = -4.5 * ((z * t) / a)
	elif z <= 6.2e-43:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * 0.5) * Float64(x / a))
	t_2 = Float64(-4.5 * Float64(t * Float64(z / a)))
	tmp = 0.0
	if (z <= -2.3e+62)
		tmp = t_2;
	elseif (z <= -1.25e-85)
		tmp = t_1;
	elseif (z <= -9.5e-119)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (z <= 6.2e-43)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * 0.5) * (x / a);
	t_2 = -4.5 * (t * (z / a));
	tmp = 0.0;
	if (z <= -2.3e+62)
		tmp = t_2;
	elseif (z <= -1.25e-85)
		tmp = t_1;
	elseif (z <= -9.5e-119)
		tmp = -4.5 * ((z * t) / a);
	elseif (z <= 6.2e-43)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * 0.5), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e+62], t$95$2, If[LessEqual[z, -1.25e-85], t$95$1, If[LessEqual[z, -9.5e-119], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e-43], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.29999999999999984e62 or 6.1999999999999999e-43 < z

   1. Initial program 89.8%

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

   3. Taylor expanded in x around 0 64.6%

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

      1. associate-*r/ 64.6%

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

      2. associate-*r* 64.6%

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

      3. associate-*l/ 67.5%

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

      4. associate-*r/ 67.5%

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

      5. associate-*l* 67.6%

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

   5. Simplified 67.6%

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

      1. associate-*l/ 64.6%

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

      2. *-commutative 64.6%

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

   7. Applied egg-rr 64.6%

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

   8. Taylor expanded in z around 0 64.6%

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

      1. associate-*r/ 67.8%

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

   10. Simplified 67.8%

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

   if -2.29999999999999984e62 < z < -1.25e-85 or -9.5000000000000002e-119 < z < 6.1999999999999999e-43

   1. Initial program 96.4%

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

   3. Taylor expanded in z around inf 87.8%

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

   4. Taylor expanded in z around 0 68.1%

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

      1. associate-*r/ 68.1%

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

      2. associate-*r* 68.1%

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

      3. associate-*l/ 66.0%

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

      4. associate-*r/ 66.0%

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

      5. *-commutative 66.0%

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

      6. associate-*r* 66.0%

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

   6. Simplified 66.0%

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

   if -1.25e-85 < z < -9.5000000000000002e-119

   1. Initial program 99.5%

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

   3. Taylor expanded in x around 0 78.1%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+62}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-85}:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-119}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-43}:\\ \;\;\;\;\left(y \cdot 0.5\right) \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+276}:\\ \;\;\;\;\frac{x \cdot y - 9 \cdot \left(z \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) (- INFINITY))
   (* 0.5 (* x (/ y a)))
   (if (<= (* x y) 5e+276)
     (/ (- (* x y) (* 9.0 (* z t))) (* a 2.0))
     (* 0.5 (/ x (/ a y))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = 0.5 * (x * (y / a));
	} else if ((x * y) <= 5e+276) {
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = 0.5 * (x * (y / a));
	} else if ((x * y) <= 5e+276) {
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
	} else {
		tmp = 0.5 * (x / (a / y));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = 0.5 * (x * (y / a))
	elif (x * y) <= 5e+276:
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0)
	else:
		tmp = 0.5 * (x / (a / y))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(0.5 * Float64(x * Float64(y / a)));
	elseif (Float64(x * y) <= 5e+276)
		tmp = Float64(Float64(Float64(x * y) - Float64(9.0 * Float64(z * t))) / Float64(a * 2.0));
	else
		tmp = Float64(0.5 * Float64(x / Float64(a / y)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -Inf)
		tmp = 0.5 * (x * (y / a));
	elseif ((x * y) <= 5e+276)
		tmp = ((x * y) - (9.0 * (z * t))) / (a * 2.0);
	else
		tmp = 0.5 * (x / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+276], N[(N[(N[(x * y), $MachinePrecision] - N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 51.8%

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

   3. Taylor expanded in x around inf 66.4%

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

      1. associate-/l* 92.8%

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

   5. Simplified 92.8%

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

   if -inf.0 < (*.f64 x y) < 5.00000000000000001e276

   1. Initial program 97.5%

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

      1. cancel-sign-sub-inv 97.5%

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

      2. fma-define 97.5%

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

      3. distribute-rgt-neg-in 97.5%

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

      4. associate-*r* 97.5%

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

      5. distribute-lft-neg-in 97.5%

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

      6. *-commutative 97.5%

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

      7. distribute-rgt-neg-in 97.5%

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

      8. metadata-eval 97.5%

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

   3. Simplified 97.5%

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

      1. *-commutative 97.5%

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

      2. associate-*r* 97.5%

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

      3. metadata-eval 97.5%

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

      4. distribute-rgt-neg-in 97.5%

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

      5. distribute-lft-neg-in 97.5%

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

      6. fma-neg 97.5%

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

      7. *-commutative 97.5%

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

      8. associate-*l* 97.5%

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

   6. Applied egg-rr 97.5%

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

   if 5.00000000000000001e276 < (*.f64 x y)

   1. Initial program 66.4%

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

      1. *-un-lft-identity 66.4%

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

      2. *-un-lft-identity 66.4%

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

      3. fma-neg 66.4%

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

      4. distribute-lft-neg-in 66.4%

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

      5. distribute-rgt-neg-in 66.4%

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

      6. metadata-eval 66.4%

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

      7. associate-*r* 66.4%

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

      8. *-commutative 66.4%

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

      9. clear-num 66.4%

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

      10. inv-pow 66.4%

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

      11. associate-/l* 66.4%

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

   4. Applied egg-rr 66.4%

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

      1. unpow-1 66.4%

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

      2. fma-define 66.4%

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

      3. +-commutative 66.4%

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

      4. fma-define 66.4%

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

   6. Simplified 66.4%

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

   7. Taylor expanded in z around 0 66.4%

      \[\leadsto \frac{1}{\color{blue}{2 \cdot \frac{a}{x \cdot y}}} \]
   8. Step-by-step derivation

      1. associate-/r* 100.0%

         \[\leadsto \frac{1}{2 \cdot \color{blue}{\frac{\frac{a}{x}}{y}}} \]

   9. Simplified 100.0%

      \[\leadsto \frac{1}{\color{blue}{2 \cdot \frac{\frac{a}{x}}{y}}} \]
   10. Step-by-step derivation

       1. *-un-lft-identity 100.0%

          \[\leadsto \color{blue}{1 \cdot \frac{1}{2 \cdot \frac{\frac{a}{x}}{y}}} \]

       2. associate-/r* 100.0%

          \[\leadsto 1 \cdot \color{blue}{\frac{\frac{1}{2}}{\frac{\frac{a}{x}}{y}}} \]

       3. metadata-eval 100.0%

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

   11. Applied egg-rr 100.0%

       \[\leadsto \color{blue}{1 \cdot \frac{0.5}{\frac{\frac{a}{x}}{y}}} \]
   12. Step-by-step derivation

       1. *-lft-identity 100.0%

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

       2. associate-/r* 66.4%

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

   13. Simplified 66.4%

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

       1. div-inv 66.4%

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

       2. clear-num 66.4%

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

       3. *-commutative 66.4%

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

       4. associate-*r/ 99.9%

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

       5. clear-num 99.9%

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

       6. un-div-inv 99.9%

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

   15. Applied egg-rr 99.9%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+276}:\\ \;\;\;\;\frac{x \cdot y - 9 \cdot \left(z \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 90.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 1.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{z \cdot \left(\frac{x \cdot y}{z} - t \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2} - t \cdot \frac{z \cdot 9}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 2.0) 1.5e+16)
   (/ (* z (- (/ (* x y) z) (* t 9.0))) (* a 2.0))
   (- (* y (/ x (* a 2.0))) (* t (/ (* z 9.0) (* a 2.0))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 2.0) <= 1.5e+16) {
		tmp = (z * (((x * y) / z) - (t * 9.0))) / (a * 2.0);
	} else {
		tmp = (y * (x / (a * 2.0))) - (t * ((z * 9.0) / (a * 2.0)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 2.0d0) <= 1.5d+16) then
        tmp = (z * (((x * y) / z) - (t * 9.0d0))) / (a * 2.0d0)
    else
        tmp = (y * (x / (a * 2.0d0))) - (t * ((z * 9.0d0) / (a * 2.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 2.0) <= 1.5e+16) {
		tmp = (z * (((x * y) / z) - (t * 9.0))) / (a * 2.0);
	} else {
		tmp = (y * (x / (a * 2.0))) - (t * ((z * 9.0) / (a * 2.0)));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (a * 2.0) <= 1.5e+16:
		tmp = (z * (((x * y) / z) - (t * 9.0))) / (a * 2.0)
	else:
		tmp = (y * (x / (a * 2.0))) - (t * ((z * 9.0) / (a * 2.0)))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 2.0) <= 1.5e+16)
		tmp = Float64(Float64(z * Float64(Float64(Float64(x * y) / z) - Float64(t * 9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(y * Float64(x / Float64(a * 2.0))) - Float64(t * Float64(Float64(z * 9.0) / Float64(a * 2.0))));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 2.0) <= 1.5e+16)
		tmp = (z * (((x * y) / z) - (t * 9.0))) / (a * 2.0);
	else
		tmp = (y * (x / (a * 2.0))) - (t * ((z * 9.0) / (a * 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 2.0), $MachinePrecision], 1.5e+16], N[(N[(z * N[(N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision] - N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(x / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(z * 9.0), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 2 binary64)) < 1.5e16

   1. Initial program 95.1%

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

   3. Taylor expanded in z around inf 91.7%

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

   if 1.5e16 < (*.f64 a #s(literal 2 binary64))

   1. Initial program 88.1%

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

      1. div-sub 88.1%

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

      2. *-commutative 88.1%

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

      3. associate-/l* 87.1%

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

      4. *-commutative 87.1%

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

      5. associate-/l* 88.4%

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

   4. Applied egg-rr 88.4%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 1.5 \cdot 10^{+16}:\\ \;\;\;\;\frac{z \cdot \left(\frac{x \cdot y}{z} - t \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2} - t \cdot \frac{z \cdot 9}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 90.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 100000:\\ \;\;\;\;\frac{z \cdot \left(\frac{x \cdot y}{z} - t \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2} - t \cdot \left(\frac{z}{a} \cdot 4.5\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 2.0) 100000.0)
   (/ (* z (- (/ (* x y) z) (* t 9.0))) (* a 2.0))
   (- (* y (/ x (* a 2.0))) (* t (* (/ z a) 4.5)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 2.0) <= 100000.0) {
		tmp = (z * (((x * y) / z) - (t * 9.0))) / (a * 2.0);
	} else {
		tmp = (y * (x / (a * 2.0))) - (t * ((z / a) * 4.5));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 2.0d0) <= 100000.0d0) then
        tmp = (z * (((x * y) / z) - (t * 9.0d0))) / (a * 2.0d0)
    else
        tmp = (y * (x / (a * 2.0d0))) - (t * ((z / a) * 4.5d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 2.0) <= 100000.0) {
		tmp = (z * (((x * y) / z) - (t * 9.0))) / (a * 2.0);
	} else {
		tmp = (y * (x / (a * 2.0))) - (t * ((z / a) * 4.5));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (a * 2.0) <= 100000.0:
		tmp = (z * (((x * y) / z) - (t * 9.0))) / (a * 2.0)
	else:
		tmp = (y * (x / (a * 2.0))) - (t * ((z / a) * 4.5))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 2.0) <= 100000.0)
		tmp = Float64(Float64(z * Float64(Float64(Float64(x * y) / z) - Float64(t * 9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(y * Float64(x / Float64(a * 2.0))) - Float64(t * Float64(Float64(z / a) * 4.5)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 2.0) <= 100000.0)
		tmp = (z * (((x * y) / z) - (t * 9.0))) / (a * 2.0);
	else
		tmp = (y * (x / (a * 2.0))) - (t * ((z / a) * 4.5));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 2.0), $MachinePrecision], 100000.0], N[(N[(z * N[(N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision] - N[(t * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(x / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(z / a), $MachinePrecision] * 4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 2 binary64)) < 1e5

   1. Initial program 95.1%

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

   3. Taylor expanded in z around inf 91.6%

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

   if 1e5 < (*.f64 a #s(literal 2 binary64))

   1. Initial program 88.6%

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

      1. div-sub 88.6%

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

      2. *-commutative 88.6%

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

      3. associate-/l* 87.6%

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

      4. *-commutative 87.6%

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

      5. associate-/l* 88.9%

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

   4. Applied egg-rr 88.9%

      \[\leadsto \color{blue}{y \cdot \frac{x}{a \cdot 2} - t \cdot \frac{z \cdot 9}{a \cdot 2}} \]
   5. Step-by-step derivation

      1. times-frac 89.0%

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

      2. metadata-eval 89.0%

         \[\leadsto y \cdot \frac{x}{a \cdot 2} - t \cdot \left(\frac{z}{a} \cdot \color{blue}{4.5}\right) \]

   6. Applied egg-rr 89.0%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 100000:\\ \;\;\;\;\frac{z \cdot \left(\frac{x \cdot y}{z} - t \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2} - t \cdot \left(\frac{z}{a} \cdot 4.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 93.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 2 \cdot 10^{-13}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2} - t \cdot \left(\frac{z}{a} \cdot 4.5\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 2.0) 2e-13)
   (/ (- (* x y) (* t (* z 9.0))) (* a 2.0))
   (- (* y (/ x (* a 2.0))) (* t (* (/ z a) 4.5)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 2.0) <= 2e-13) {
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0);
	} else {
		tmp = (y * (x / (a * 2.0))) - (t * ((z / a) * 4.5));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 2.0d0) <= 2d-13) then
        tmp = ((x * y) - (t * (z * 9.0d0))) / (a * 2.0d0)
    else
        tmp = (y * (x / (a * 2.0d0))) - (t * ((z / a) * 4.5d0))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 2.0) <= 2e-13) {
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0);
	} else {
		tmp = (y * (x / (a * 2.0))) - (t * ((z / a) * 4.5));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (a * 2.0) <= 2e-13:
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0)
	else:
		tmp = (y * (x / (a * 2.0))) - (t * ((z / a) * 4.5))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 2.0) <= 2e-13)
		tmp = Float64(Float64(Float64(x * y) - Float64(t * Float64(z * 9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(y * Float64(x / Float64(a * 2.0))) - Float64(t * Float64(Float64(z / a) * 4.5)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 2.0) <= 2e-13)
		tmp = ((x * y) - (t * (z * 9.0))) / (a * 2.0);
	else
		tmp = (y * (x / (a * 2.0))) - (t * ((z / a) * 4.5));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 2.0), $MachinePrecision], 2e-13], N[(N[(N[(x * y), $MachinePrecision] - N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(x / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(z / a), $MachinePrecision] * 4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 2 binary64)) < 2.0000000000000001e-13

   1. Initial program 95.0%

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

   if 2.0000000000000001e-13 < (*.f64 a #s(literal 2 binary64))

   1. Initial program 88.8%

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

      1. div-sub 88.7%

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

      2. *-commutative 88.7%

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

      3. associate-/l* 87.8%

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

      4. *-commutative 87.8%

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

      5. associate-/l* 89.1%

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

   4. Applied egg-rr 89.1%

      \[\leadsto \color{blue}{y \cdot \frac{x}{a \cdot 2} - t \cdot \frac{z \cdot 9}{a \cdot 2}} \]
   5. Step-by-step derivation

      1. times-frac 89.1%

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

      2. metadata-eval 89.1%

         \[\leadsto y \cdot \frac{x}{a \cdot 2} - t \cdot \left(\frac{z}{a} \cdot \color{blue}{4.5}\right) \]

   6. Applied egg-rr 89.1%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 2 \cdot 10^{-13}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a \cdot 2} - t \cdot \left(\frac{z}{a} \cdot 4.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 68.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+62} \lor \neg \left(z \leq 7 \cdot 10^{-42}\right):\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (<= z -1.25e+62) (not (<= z 7e-42)))
   (* -4.5 (* t (/ z a)))
   (* 0.5 (* x (/ y a)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.25e+62) || !(z <= 7e-42)) {
		tmp = -4.5 * (t * (z / a));
	} 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.
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 <= (-1.25d+62)) .or. (.not. (z <= 7d-42))) then
        tmp = (-4.5d0) * (t * (z / a))
    else
        tmp = 0.5d0 * (x * (y / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.25e+62) || !(z <= 7e-42)) {
		tmp = -4.5 * (t * (z / a));
	} else {
		tmp = 0.5 * (x * (y / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.25e+62) or not (z <= 7e-42):
		tmp = -4.5 * (t * (z / a))
	else:
		tmp = 0.5 * (x * (y / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.25e+62) || !(z <= 7e-42))
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	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])){:}
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 <= -1.25e+62) || ~((z <= 7e-42)))
		tmp = -4.5 * (t * (z / a));
	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.
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[z, -1.25e+62], N[Not[LessEqual[z, 7e-42]], $MachinePrecision]], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25000000000000007e62 or 7.0000000000000004e-42 < z

   1. Initial program 89.8%

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

   3. Taylor expanded in x around 0 64.6%

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

      1. associate-*r/ 64.6%

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

      2. associate-*r* 64.6%

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

      3. associate-*l/ 67.5%

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

      4. associate-*r/ 67.5%

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

      5. associate-*l* 67.6%

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

   5. Simplified 67.6%

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

      1. associate-*l/ 64.6%

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

      2. *-commutative 64.6%

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

   7. Applied egg-rr 64.6%

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

   8. Taylor expanded in z around 0 64.6%

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

      1. associate-*r/ 67.8%

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

   10. Simplified 67.8%

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

   if -1.25000000000000007e62 < z < 7.0000000000000004e-42

   1. Initial program 96.7%

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

   3. Taylor expanded in x around inf 66.9%

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

      1. associate-/l* 61.9%

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

   5. Simplified 61.9%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+62} \lor \neg \left(z \leq 7 \cdot 10^{-42}\right):\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.1% accurate, 1.9× speedup

Math

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

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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);
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.
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;
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])
[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])
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])){:}
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.
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 93.3%

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

3. Taylor expanded in x around 0 54.1%

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

   1. associate-*r/ 54.0%

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

   2. associate-*r* 54.0%

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

   3. associate-*l/ 53.9%

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

   4. associate-*r/ 53.9%

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

   5. associate-*l* 54.1%

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

5. Simplified 54.1%

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

   1. associate-*l/ 54.1%

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

   2. *-commutative 54.1%

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

7. Applied egg-rr 54.1%

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

8. Taylor expanded in z around 0 54.1%

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

   1. associate-*r/ 53.2%

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

10. Simplified 53.2%

    \[\leadsto -4.5 \cdot \color{blue}{\left(t \cdot \frac{z}{a}\right)} \]
11. 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 2024101 
(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)))