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

Percentage Accurate: 91.2% → 93.2%

Time: 13.2s

Alternatives: 14

Speedup: 1.0×

• 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: 93.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - t \cdot \left(z \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq 10^{+228}:\\ \;\;\;\;\frac{t\_1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\frac{x}{2}}{a} - \left(z \cdot 9\right) \cdot \frac{t}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* t (* z 9.0)))))
   (if (<= t_1 1e+228)
     (/ t_1 (* a 2.0))
     (- (* y (/ (/ x 2.0) a)) (* (* z 9.0) (/ t (* a 2.0)))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (t * (z * 9.0));
	double tmp;
	if (t_1 <= 1e+228) {
		tmp = t_1 / (a * 2.0);
	} else {
		tmp = (y * ((x / 2.0) / a)) - ((z * 9.0) * (t / (a * 2.0)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - (t * (z * 9.0d0))
    if (t_1 <= 1d+228) then
        tmp = t_1 / (a * 2.0d0)
    else
        tmp = (y * ((x / 2.0d0) / a)) - ((z * 9.0d0) * (t / (a * 2.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (t * (z * 9.0));
	double tmp;
	if (t_1 <= 1e+228) {
		tmp = t_1 / (a * 2.0);
	} else {
		tmp = (y * ((x / 2.0) / a)) - ((z * 9.0) * (t / (a * 2.0)));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - (t * (z * 9.0))
	tmp = 0
	if t_1 <= 1e+228:
		tmp = t_1 / (a * 2.0)
	else:
		tmp = (y * ((x / 2.0) / a)) - ((z * 9.0) * (t / (a * 2.0)))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(t * Float64(z * 9.0)))
	tmp = 0.0
	if (t_1 <= 1e+228)
		tmp = Float64(t_1 / Float64(a * 2.0));
	else
		tmp = Float64(Float64(y * Float64(Float64(x / 2.0) / a)) - Float64(Float64(z * 9.0) * Float64(t / Float64(a * 2.0))));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (t * (z * 9.0));
	tmp = 0.0;
	if (t_1 <= 1e+228)
		tmp = t_1 / (a * 2.0);
	else
		tmp = (y * ((x / 2.0) / a)) - ((z * 9.0) * (t / (a * 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+228], N[(t$95$1 / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(x / 2.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * N[(t / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 9.9999999999999992e227

   1. Initial program 96.9%

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

   if 9.9999999999999992e227 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 78.7%

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

      1. div-sub 73.8%

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

      2. associate-/l* 78.4%

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

      3. associate-/l* 90.2%

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

   4. Applied egg-rr 90.2%

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

      1. clear-num 90.2%

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

      2. un-div-inv 90.2%

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

      3. *-commutative 90.2%

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

      4. *-un-lft-identity 90.2%

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

      5. times-frac 90.2%

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

      6. metadata-eval 90.2%

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

   6. Applied egg-rr 90.2%

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

      1. associate-/r* 90.2%

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

      2. associate-/r/ 90.2%

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

   8. Simplified 90.2%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - t \cdot \left(z \cdot 9\right) \leq 10^{+228}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\frac{x}{2}}{a} - \left(z \cdot 9\right) \cdot \frac{t}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.7% accurate, 0.1× speedup

Math

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

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

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(fma(x, y, Float64(z * Float64(t * -9.0))) / Float64(a * 2.0))
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[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.0%

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

   1. div-sub 91.7%

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

   2. *-commutative 91.7%

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

   3. div-sub 94.0%

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

   4. cancel-sign-sub-inv 94.0%

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

   5. *-commutative 94.0%

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

   6. fma-define 94.4%

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

   7. distribute-rgt-neg-in 94.4%

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

   8. associate-*r* 94.4%

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

   9. distribute-lft-neg-in 94.4%

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

   10. *-commutative 94.4%

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

   11. distribute-rgt-neg-in 94.4%

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

   12. metadata-eval 94.4%

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

3. Simplified 94.4%

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

5. Final simplification 94.4%

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

Alternative 3: 91.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \mathsf{fma}\left(t, z \cdot -9, x \cdot y\right) \cdot \frac{0.5}{a} \end{array} \]

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
 (* (fma t (* z -9.0) (* x y)) (/ 0.5 a)))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	return fma(t, (z * -9.0), (x * y)) * (0.5 / 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(fma(t, Float64(z * -9.0), Float64(x * y)) * Float64(0.5 / 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[(N[(t * N[(z * -9.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.0%

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

3. Taylor expanded in a around 0 94.1%

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

   1. associate-*r/ 94.1%

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

   2. cancel-sign-sub-inv 94.1%

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

   3. metadata-eval 94.1%

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

   4. *-commutative 94.1%

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

   5. associate-*r* 94.0%

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

   6. fma-define 94.4%

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

   7. associate-*l/ 94.3%

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

   8. *-commutative 94.3%

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

   9. fma-define 93.9%

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

   10. +-commutative 93.9%

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

   11. fma-define 94.4%

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

5. Simplified 94.4%

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

6. Final simplification 94.4%

   \[\leadsto \mathsf{fma}\left(t, z \cdot -9, x \cdot y\right) \cdot \frac{0.5}{a} \]
7. Add Preprocessing

Alternative 4: 71.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{+55}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-27}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+70}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 \cdot \frac{y}{a}\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (/ 0.5 (/ a (* x y)))))
   (if (<= (* x y) -2e+87)
     t_1
     (if (<= (* x y) -4e+55)
       (* -4.5 (/ z (/ a t)))
       (if (<= (* x y) -2e+35)
         t_1
         (if (<= (* x y) 5e-27)
           (* -4.5 (/ (* z t) a))
           (if (<= (* x y) 1e+59)
             t_1
             (if (<= (* x y) 2e+70)
               (* -4.5 (* z (/ t a)))
               (* x (* 0.5 (/ 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 t_1 = 0.5 / (a / (x * y));
	double tmp;
	if ((x * y) <= -2e+87) {
		tmp = t_1;
	} else if ((x * y) <= -4e+55) {
		tmp = -4.5 * (z / (a / t));
	} else if ((x * y) <= -2e+35) {
		tmp = t_1;
	} else if ((x * y) <= 5e-27) {
		tmp = -4.5 * ((z * t) / a);
	} else if ((x * y) <= 1e+59) {
		tmp = t_1;
	} else if ((x * y) <= 2e+70) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = x * (0.5 * (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) :: t_1
    real(8) :: tmp
    t_1 = 0.5d0 / (a / (x * y))
    if ((x * y) <= (-2d+87)) then
        tmp = t_1
    else if ((x * y) <= (-4d+55)) then
        tmp = (-4.5d0) * (z / (a / t))
    else if ((x * y) <= (-2d+35)) then
        tmp = t_1
    else if ((x * y) <= 5d-27) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if ((x * y) <= 1d+59) then
        tmp = t_1
    else if ((x * y) <= 2d+70) then
        tmp = (-4.5d0) * (z * (t / a))
    else
        tmp = x * (0.5d0 * (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 t_1 = 0.5 / (a / (x * y));
	double tmp;
	if ((x * y) <= -2e+87) {
		tmp = t_1;
	} else if ((x * y) <= -4e+55) {
		tmp = -4.5 * (z / (a / t));
	} else if ((x * y) <= -2e+35) {
		tmp = t_1;
	} else if ((x * y) <= 5e-27) {
		tmp = -4.5 * ((z * t) / a);
	} else if ((x * y) <= 1e+59) {
		tmp = t_1;
	} else if ((x * y) <= 2e+70) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = x * (0.5 * (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):
	t_1 = 0.5 / (a / (x * y))
	tmp = 0
	if (x * y) <= -2e+87:
		tmp = t_1
	elif (x * y) <= -4e+55:
		tmp = -4.5 * (z / (a / t))
	elif (x * y) <= -2e+35:
		tmp = t_1
	elif (x * y) <= 5e-27:
		tmp = -4.5 * ((z * t) / a)
	elif (x * y) <= 1e+59:
		tmp = t_1
	elif (x * y) <= 2e+70:
		tmp = -4.5 * (z * (t / a))
	else:
		tmp = x * (0.5 * (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)
	t_1 = Float64(0.5 / Float64(a / Float64(x * y)))
	tmp = 0.0
	if (Float64(x * y) <= -2e+87)
		tmp = t_1;
	elseif (Float64(x * y) <= -4e+55)
		tmp = Float64(-4.5 * Float64(z / Float64(a / t)));
	elseif (Float64(x * y) <= -2e+35)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-27)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (Float64(x * y) <= 1e+59)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e+70)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	else
		tmp = Float64(x * Float64(0.5 * 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)
	t_1 = 0.5 / (a / (x * y));
	tmp = 0.0;
	if ((x * y) <= -2e+87)
		tmp = t_1;
	elseif ((x * y) <= -4e+55)
		tmp = -4.5 * (z / (a / t));
	elseif ((x * y) <= -2e+35)
		tmp = t_1;
	elseif ((x * y) <= 5e-27)
		tmp = -4.5 * ((z * t) / a);
	elseif ((x * y) <= 1e+59)
		tmp = t_1;
	elseif ((x * y) <= 2e+70)
		tmp = -4.5 * (z * (t / a));
	else
		tmp = x * (0.5 * (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_] := Block[{t$95$1 = N[(0.5 / N[(a / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+87], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -4e+55], N[(-4.5 * N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e+35], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-27], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+59], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e+70], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(0.5 * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -1.9999999999999999e87 or -4.00000000000000004e55 < (*.f64 x y) < -1.9999999999999999e35 or 5.0000000000000002e-27 < (*.f64 x y) < 9.99999999999999972e58

   1. Initial program 92.3%

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

      1. clear-num 92.2%

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

      2. inv-pow 92.2%

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

      3. *-commutative 92.2%

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

      4. associate-/l* 92.2%

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

      5. fma-neg 93.5%

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

      6. *-commutative 93.5%

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

      7. distribute-rgt-neg-in 93.5%

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

      8. distribute-rgt-neg-in 93.5%

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

      9. metadata-eval 93.5%

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

   4. Applied egg-rr 93.5%

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

      1. unpow-1 93.5%

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

      2. associate-/r* 93.5%

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

      3. metadata-eval 93.5%

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

      4. fma-define 92.2%

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

      5. +-commutative 92.2%

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

      6. fma-define 93.5%

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

   6. Simplified 93.5%

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

   7. Taylor expanded in t around 0 80.2%

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

   if -1.9999999999999999e87 < (*.f64 x y) < -4.00000000000000004e55

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 75.5%

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

      1. *-commutative 75.5%

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

      2. associate-/l* 75.5%

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

   5. Applied egg-rr 75.5%

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

      1. clear-num 75.5%

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

      2. un-div-inv 75.5%

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

   7. Applied egg-rr 75.5%

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

   if -1.9999999999999999e35 < (*.f64 x y) < 5.0000000000000002e-27

   1. Initial program 95.7%

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

   3. Taylor expanded in x around 0 79.2%

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

   if 9.99999999999999972e58 < (*.f64 x y) < 2.00000000000000015e70

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 100.0%

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

   5. Applied egg-rr 100.0%

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

   if 2.00000000000000015e70 < (*.f64 x y)

   1. Initial program 91.1%

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

   3. Taylor expanded in x around inf 77.9%

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

      1. *-commutative 77.9%

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

      2. associate-/l* 76.0%

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

      3. associate-*l* 76.0%

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

   5. Simplified 76.0%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+87}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{+55}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+35}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-27}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+59}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+70}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 \cdot \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+87}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{+55}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-27}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+70}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 \cdot \frac{y}{a}\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (/ 0.5 (/ a (* x y)))))
   (if (<= (* x y) -2e+87)
     (/ (* x y) (* a 2.0))
     (if (<= (* x y) -4e+55)
       (* -4.5 (/ z (/ a t)))
       (if (<= (* x y) -2e+35)
         t_1
         (if (<= (* x y) 5e-27)
           (* -4.5 (/ (* z t) a))
           (if (<= (* x y) 1e+59)
             t_1
             (if (<= (* x y) 2e+70)
               (* -4.5 (* z (/ t a)))
               (* x (* 0.5 (/ 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 t_1 = 0.5 / (a / (x * y));
	double tmp;
	if ((x * y) <= -2e+87) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= -4e+55) {
		tmp = -4.5 * (z / (a / t));
	} else if ((x * y) <= -2e+35) {
		tmp = t_1;
	} else if ((x * y) <= 5e-27) {
		tmp = -4.5 * ((z * t) / a);
	} else if ((x * y) <= 1e+59) {
		tmp = t_1;
	} else if ((x * y) <= 2e+70) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = x * (0.5 * (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) :: t_1
    real(8) :: tmp
    t_1 = 0.5d0 / (a / (x * y))
    if ((x * y) <= (-2d+87)) then
        tmp = (x * y) / (a * 2.0d0)
    else if ((x * y) <= (-4d+55)) then
        tmp = (-4.5d0) * (z / (a / t))
    else if ((x * y) <= (-2d+35)) then
        tmp = t_1
    else if ((x * y) <= 5d-27) then
        tmp = (-4.5d0) * ((z * t) / a)
    else if ((x * y) <= 1d+59) then
        tmp = t_1
    else if ((x * y) <= 2d+70) then
        tmp = (-4.5d0) * (z * (t / a))
    else
        tmp = x * (0.5d0 * (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 t_1 = 0.5 / (a / (x * y));
	double tmp;
	if ((x * y) <= -2e+87) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= -4e+55) {
		tmp = -4.5 * (z / (a / t));
	} else if ((x * y) <= -2e+35) {
		tmp = t_1;
	} else if ((x * y) <= 5e-27) {
		tmp = -4.5 * ((z * t) / a);
	} else if ((x * y) <= 1e+59) {
		tmp = t_1;
	} else if ((x * y) <= 2e+70) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = x * (0.5 * (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):
	t_1 = 0.5 / (a / (x * y))
	tmp = 0
	if (x * y) <= -2e+87:
		tmp = (x * y) / (a * 2.0)
	elif (x * y) <= -4e+55:
		tmp = -4.5 * (z / (a / t))
	elif (x * y) <= -2e+35:
		tmp = t_1
	elif (x * y) <= 5e-27:
		tmp = -4.5 * ((z * t) / a)
	elif (x * y) <= 1e+59:
		tmp = t_1
	elif (x * y) <= 2e+70:
		tmp = -4.5 * (z * (t / a))
	else:
		tmp = x * (0.5 * (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)
	t_1 = Float64(0.5 / Float64(a / Float64(x * y)))
	tmp = 0.0
	if (Float64(x * y) <= -2e+87)
		tmp = Float64(Float64(x * y) / Float64(a * 2.0));
	elseif (Float64(x * y) <= -4e+55)
		tmp = Float64(-4.5 * Float64(z / Float64(a / t)));
	elseif (Float64(x * y) <= -2e+35)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-27)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	elseif (Float64(x * y) <= 1e+59)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e+70)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	else
		tmp = Float64(x * Float64(0.5 * 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)
	t_1 = 0.5 / (a / (x * y));
	tmp = 0.0;
	if ((x * y) <= -2e+87)
		tmp = (x * y) / (a * 2.0);
	elseif ((x * y) <= -4e+55)
		tmp = -4.5 * (z / (a / t));
	elseif ((x * y) <= -2e+35)
		tmp = t_1;
	elseif ((x * y) <= 5e-27)
		tmp = -4.5 * ((z * t) / a);
	elseif ((x * y) <= 1e+59)
		tmp = t_1;
	elseif ((x * y) <= 2e+70)
		tmp = -4.5 * (z * (t / a));
	else
		tmp = x * (0.5 * (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_] := Block[{t$95$1 = N[(0.5 / N[(a / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+87], N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4e+55], N[(-4.5 * N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e+35], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-27], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+59], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e+70], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(0.5 * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 x y) < -1.9999999999999999e87

   1. Initial program 91.1%

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

   3. Taylor expanded in x around inf 84.0%

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

   if -1.9999999999999999e87 < (*.f64 x y) < -4.00000000000000004e55

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 75.5%

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

      1. *-commutative 75.5%

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

      2. associate-/l* 75.5%

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

   5. Applied egg-rr 75.5%

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

      1. clear-num 75.5%

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

      2. un-div-inv 75.5%

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

   7. Applied egg-rr 75.5%

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

   if -4.00000000000000004e55 < (*.f64 x y) < -1.9999999999999999e35 or 5.0000000000000002e-27 < (*.f64 x y) < 9.99999999999999972e58

   1. Initial program 95.4%

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

      1. clear-num 95.5%

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

      2. inv-pow 95.5%

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

      3. *-commutative 95.5%

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

      4. associate-/l* 95.5%

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

      5. fma-neg 95.5%

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

      6. *-commutative 95.5%

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

      7. distribute-rgt-neg-in 95.5%

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

      8. distribute-rgt-neg-in 95.5%

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

      9. metadata-eval 95.5%

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

   4. Applied egg-rr 95.5%

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

      1. unpow-1 95.5%

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

      2. associate-/r* 95.5%

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

      3. metadata-eval 95.5%

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

      4. fma-define 95.5%

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

      5. +-commutative 95.5%

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

      6. fma-define 95.5%

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

   6. Simplified 95.5%

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

   7. Taylor expanded in t around 0 71.0%

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

   if -1.9999999999999999e35 < (*.f64 x y) < 5.0000000000000002e-27

   1. Initial program 95.7%

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

   3. Taylor expanded in x around 0 79.2%

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

   if 9.99999999999999972e58 < (*.f64 x y) < 2.00000000000000015e70

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 100.0%

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

   5. Applied egg-rr 100.0%

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

   if 2.00000000000000015e70 < (*.f64 x y)

   1. Initial program 91.1%

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

   3. Taylor expanded in x around inf 77.9%

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

      1. *-commutative 77.9%

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

      2. associate-/l* 76.0%

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

      3. associate-*l* 76.0%

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

   5. Simplified 76.0%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+87}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{+55}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+35}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-27}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+59}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+70}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 \cdot \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+87}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{+55}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-27}:\\ \;\;\;\;\frac{-4.5 \cdot \left(z \cdot t\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+70}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 \cdot \frac{y}{a}\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (/ 0.5 (/ a (* x y)))))
   (if (<= (* x y) -2e+87)
     (/ (* x y) (* a 2.0))
     (if (<= (* x y) -4e+55)
       (* -4.5 (/ z (/ a t)))
       (if (<= (* x y) -2e+35)
         t_1
         (if (<= (* x y) 5e-27)
           (/ (* -4.5 (* z t)) a)
           (if (<= (* x y) 1e+59)
             t_1
             (if (<= (* x y) 2e+70)
               (* -4.5 (* z (/ t a)))
               (* x (* 0.5 (/ 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 t_1 = 0.5 / (a / (x * y));
	double tmp;
	if ((x * y) <= -2e+87) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= -4e+55) {
		tmp = -4.5 * (z / (a / t));
	} else if ((x * y) <= -2e+35) {
		tmp = t_1;
	} else if ((x * y) <= 5e-27) {
		tmp = (-4.5 * (z * t)) / a;
	} else if ((x * y) <= 1e+59) {
		tmp = t_1;
	} else if ((x * y) <= 2e+70) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = x * (0.5 * (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) :: t_1
    real(8) :: tmp
    t_1 = 0.5d0 / (a / (x * y))
    if ((x * y) <= (-2d+87)) then
        tmp = (x * y) / (a * 2.0d0)
    else if ((x * y) <= (-4d+55)) then
        tmp = (-4.5d0) * (z / (a / t))
    else if ((x * y) <= (-2d+35)) then
        tmp = t_1
    else if ((x * y) <= 5d-27) then
        tmp = ((-4.5d0) * (z * t)) / a
    else if ((x * y) <= 1d+59) then
        tmp = t_1
    else if ((x * y) <= 2d+70) then
        tmp = (-4.5d0) * (z * (t / a))
    else
        tmp = x * (0.5d0 * (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 t_1 = 0.5 / (a / (x * y));
	double tmp;
	if ((x * y) <= -2e+87) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= -4e+55) {
		tmp = -4.5 * (z / (a / t));
	} else if ((x * y) <= -2e+35) {
		tmp = t_1;
	} else if ((x * y) <= 5e-27) {
		tmp = (-4.5 * (z * t)) / a;
	} else if ((x * y) <= 1e+59) {
		tmp = t_1;
	} else if ((x * y) <= 2e+70) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = x * (0.5 * (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):
	t_1 = 0.5 / (a / (x * y))
	tmp = 0
	if (x * y) <= -2e+87:
		tmp = (x * y) / (a * 2.0)
	elif (x * y) <= -4e+55:
		tmp = -4.5 * (z / (a / t))
	elif (x * y) <= -2e+35:
		tmp = t_1
	elif (x * y) <= 5e-27:
		tmp = (-4.5 * (z * t)) / a
	elif (x * y) <= 1e+59:
		tmp = t_1
	elif (x * y) <= 2e+70:
		tmp = -4.5 * (z * (t / a))
	else:
		tmp = x * (0.5 * (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)
	t_1 = Float64(0.5 / Float64(a / Float64(x * y)))
	tmp = 0.0
	if (Float64(x * y) <= -2e+87)
		tmp = Float64(Float64(x * y) / Float64(a * 2.0));
	elseif (Float64(x * y) <= -4e+55)
		tmp = Float64(-4.5 * Float64(z / Float64(a / t)));
	elseif (Float64(x * y) <= -2e+35)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-27)
		tmp = Float64(Float64(-4.5 * Float64(z * t)) / a);
	elseif (Float64(x * y) <= 1e+59)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e+70)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	else
		tmp = Float64(x * Float64(0.5 * 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)
	t_1 = 0.5 / (a / (x * y));
	tmp = 0.0;
	if ((x * y) <= -2e+87)
		tmp = (x * y) / (a * 2.0);
	elseif ((x * y) <= -4e+55)
		tmp = -4.5 * (z / (a / t));
	elseif ((x * y) <= -2e+35)
		tmp = t_1;
	elseif ((x * y) <= 5e-27)
		tmp = (-4.5 * (z * t)) / a;
	elseif ((x * y) <= 1e+59)
		tmp = t_1;
	elseif ((x * y) <= 2e+70)
		tmp = -4.5 * (z * (t / a));
	else
		tmp = x * (0.5 * (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_] := Block[{t$95$1 = N[(0.5 / N[(a / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+87], N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4e+55], N[(-4.5 * N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e+35], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-27], N[(N[(-4.5 * N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+59], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e+70], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(0.5 * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 x y) < -1.9999999999999999e87

   1. Initial program 91.1%

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

   3. Taylor expanded in x around inf 84.0%

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

   if -1.9999999999999999e87 < (*.f64 x y) < -4.00000000000000004e55

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 75.5%

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

      1. *-commutative 75.5%

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

      2. associate-/l* 75.5%

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

   5. Applied egg-rr 75.5%

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

      1. clear-num 75.5%

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

      2. un-div-inv 75.5%

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

   7. Applied egg-rr 75.5%

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

   if -4.00000000000000004e55 < (*.f64 x y) < -1.9999999999999999e35 or 5.0000000000000002e-27 < (*.f64 x y) < 9.99999999999999972e58

   1. Initial program 95.4%

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

      1. clear-num 95.5%

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

      2. inv-pow 95.5%

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

      3. *-commutative 95.5%

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

      4. associate-/l* 95.5%

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

      5. fma-neg 95.5%

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

      6. *-commutative 95.5%

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

      7. distribute-rgt-neg-in 95.5%

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

      8. distribute-rgt-neg-in 95.5%

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

      9. metadata-eval 95.5%

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

   4. Applied egg-rr 95.5%

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

      1. unpow-1 95.5%

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

      2. associate-/r* 95.5%

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

      3. metadata-eval 95.5%

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

      4. fma-define 95.5%

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

      5. +-commutative 95.5%

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

      6. fma-define 95.5%

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

   6. Simplified 95.5%

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

   7. Taylor expanded in t around 0 71.0%

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

   if -1.9999999999999999e35 < (*.f64 x y) < 5.0000000000000002e-27

   1. Initial program 95.7%

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

   3. Taylor expanded in x around 0 79.2%

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

      1. *-commutative 79.2%

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

      2. associate-*l/ 79.2%

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

   5. Applied egg-rr 79.2%

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

   if 9.99999999999999972e58 < (*.f64 x y) < 2.00000000000000015e70

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 100.0%

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

   5. Applied egg-rr 100.0%

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

   if 2.00000000000000015e70 < (*.f64 x y)

   1. Initial program 91.1%

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

   3. Taylor expanded in x around inf 77.9%

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

      1. *-commutative 77.9%

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

      2. associate-/l* 76.0%

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

      3. associate-*l* 76.0%

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

   5. Simplified 76.0%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+87}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{+55}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+35}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-27}:\\ \;\;\;\;\frac{-4.5 \cdot \left(z \cdot t\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+59}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+70}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 \cdot \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+87}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{+55}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-27}:\\ \;\;\;\;\frac{-9 \cdot \left(z \cdot t\right)}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+70}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 \cdot \frac{y}{a}\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (/ 0.5 (/ a (* x y)))))
   (if (<= (* x y) -2e+87)
     (/ (* x y) (* a 2.0))
     (if (<= (* x y) -4e+55)
       (* -4.5 (/ z (/ a t)))
       (if (<= (* x y) -2e+35)
         t_1
         (if (<= (* x y) 5e-27)
           (/ (* -9.0 (* z t)) (* a 2.0))
           (if (<= (* x y) 1e+59)
             t_1
             (if (<= (* x y) 2e+70)
               (* -4.5 (* z (/ t a)))
               (* x (* 0.5 (/ 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 t_1 = 0.5 / (a / (x * y));
	double tmp;
	if ((x * y) <= -2e+87) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= -4e+55) {
		tmp = -4.5 * (z / (a / t));
	} else if ((x * y) <= -2e+35) {
		tmp = t_1;
	} else if ((x * y) <= 5e-27) {
		tmp = (-9.0 * (z * t)) / (a * 2.0);
	} else if ((x * y) <= 1e+59) {
		tmp = t_1;
	} else if ((x * y) <= 2e+70) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = x * (0.5 * (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) :: t_1
    real(8) :: tmp
    t_1 = 0.5d0 / (a / (x * y))
    if ((x * y) <= (-2d+87)) then
        tmp = (x * y) / (a * 2.0d0)
    else if ((x * y) <= (-4d+55)) then
        tmp = (-4.5d0) * (z / (a / t))
    else if ((x * y) <= (-2d+35)) then
        tmp = t_1
    else if ((x * y) <= 5d-27) then
        tmp = ((-9.0d0) * (z * t)) / (a * 2.0d0)
    else if ((x * y) <= 1d+59) then
        tmp = t_1
    else if ((x * y) <= 2d+70) then
        tmp = (-4.5d0) * (z * (t / a))
    else
        tmp = x * (0.5d0 * (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 t_1 = 0.5 / (a / (x * y));
	double tmp;
	if ((x * y) <= -2e+87) {
		tmp = (x * y) / (a * 2.0);
	} else if ((x * y) <= -4e+55) {
		tmp = -4.5 * (z / (a / t));
	} else if ((x * y) <= -2e+35) {
		tmp = t_1;
	} else if ((x * y) <= 5e-27) {
		tmp = (-9.0 * (z * t)) / (a * 2.0);
	} else if ((x * y) <= 1e+59) {
		tmp = t_1;
	} else if ((x * y) <= 2e+70) {
		tmp = -4.5 * (z * (t / a));
	} else {
		tmp = x * (0.5 * (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):
	t_1 = 0.5 / (a / (x * y))
	tmp = 0
	if (x * y) <= -2e+87:
		tmp = (x * y) / (a * 2.0)
	elif (x * y) <= -4e+55:
		tmp = -4.5 * (z / (a / t))
	elif (x * y) <= -2e+35:
		tmp = t_1
	elif (x * y) <= 5e-27:
		tmp = (-9.0 * (z * t)) / (a * 2.0)
	elif (x * y) <= 1e+59:
		tmp = t_1
	elif (x * y) <= 2e+70:
		tmp = -4.5 * (z * (t / a))
	else:
		tmp = x * (0.5 * (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)
	t_1 = Float64(0.5 / Float64(a / Float64(x * y)))
	tmp = 0.0
	if (Float64(x * y) <= -2e+87)
		tmp = Float64(Float64(x * y) / Float64(a * 2.0));
	elseif (Float64(x * y) <= -4e+55)
		tmp = Float64(-4.5 * Float64(z / Float64(a / t)));
	elseif (Float64(x * y) <= -2e+35)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-27)
		tmp = Float64(Float64(-9.0 * Float64(z * t)) / Float64(a * 2.0));
	elseif (Float64(x * y) <= 1e+59)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e+70)
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	else
		tmp = Float64(x * Float64(0.5 * 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)
	t_1 = 0.5 / (a / (x * y));
	tmp = 0.0;
	if ((x * y) <= -2e+87)
		tmp = (x * y) / (a * 2.0);
	elseif ((x * y) <= -4e+55)
		tmp = -4.5 * (z / (a / t));
	elseif ((x * y) <= -2e+35)
		tmp = t_1;
	elseif ((x * y) <= 5e-27)
		tmp = (-9.0 * (z * t)) / (a * 2.0);
	elseif ((x * y) <= 1e+59)
		tmp = t_1;
	elseif ((x * y) <= 2e+70)
		tmp = -4.5 * (z * (t / a));
	else
		tmp = x * (0.5 * (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_] := Block[{t$95$1 = N[(0.5 / N[(a / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+87], N[(N[(x * y), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -4e+55], N[(-4.5 * N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e+35], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-27], N[(N[(-9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+59], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e+70], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(0.5 * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 x y) < -1.9999999999999999e87

   1. Initial program 91.1%

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

   3. Taylor expanded in x around inf 84.0%

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

   if -1.9999999999999999e87 < (*.f64 x y) < -4.00000000000000004e55

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 75.5%

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

      1. *-commutative 75.5%

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

      2. associate-/l* 75.5%

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

   5. Applied egg-rr 75.5%

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

      1. clear-num 75.5%

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

      2. un-div-inv 75.5%

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

   7. Applied egg-rr 75.5%

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

   if -4.00000000000000004e55 < (*.f64 x y) < -1.9999999999999999e35 or 5.0000000000000002e-27 < (*.f64 x y) < 9.99999999999999972e58

   1. Initial program 95.4%

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

      1. clear-num 95.5%

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

      2. inv-pow 95.5%

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

      3. *-commutative 95.5%

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

      4. associate-/l* 95.5%

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

      5. fma-neg 95.5%

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

      6. *-commutative 95.5%

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

      7. distribute-rgt-neg-in 95.5%

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

      8. distribute-rgt-neg-in 95.5%

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

      9. metadata-eval 95.5%

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

   4. Applied egg-rr 95.5%

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

      1. unpow-1 95.5%

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

      2. associate-/r* 95.5%

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

      3. metadata-eval 95.5%

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

      4. fma-define 95.5%

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

      5. +-commutative 95.5%

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

      6. fma-define 95.5%

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

   6. Simplified 95.5%

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

   7. Taylor expanded in t around 0 71.0%

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

   if -1.9999999999999999e35 < (*.f64 x y) < 5.0000000000000002e-27

   1. Initial program 95.7%

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

   3. Taylor expanded in x around 0 79.2%

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

   if 9.99999999999999972e58 < (*.f64 x y) < 2.00000000000000015e70

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 100.0%

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

   5. Applied egg-rr 100.0%

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

   if 2.00000000000000015e70 < (*.f64 x y)

   1. Initial program 91.1%

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

   3. Taylor expanded in x around inf 77.9%

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

      1. *-commutative 77.9%

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

      2. associate-/l* 76.0%

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

      3. associate-*l* 76.0%

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

   5. Simplified 76.0%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{a} \cdot 0.5\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+87}:\\ \;\;\;\;\frac{x \cdot y}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq -4 \cdot 10^{+55}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{+35}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-27}:\\ \;\;\;\;\frac{-9 \cdot \left(z \cdot t\right)}{a \cdot 2}\\ \mathbf{elif}\;x \cdot y \leq 10^{+59}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+70}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 \cdot \frac{y}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 93.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - t \cdot \left(z \cdot 9\right)\\ \mathbf{if}\;t\_1 \leq 10^{+228}:\\ \;\;\;\;\frac{t\_1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2} - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array} \end{array} \]

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
 (let* ((t_1 (- (* x y) (* t (* z 9.0)))))
   (if (<= t_1 1e+228)
     (/ t_1 (* a 2.0))
     (- (* x (/ y (* a 2.0))) (* (/ t a) (* z 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 t_1 = (x * y) - (t * (z * 9.0));
	double tmp;
	if (t_1 <= 1e+228) {
		tmp = t_1 / (a * 2.0);
	} else {
		tmp = (x * (y / (a * 2.0))) - ((t / a) * (z * 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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - (t * (z * 9.0d0))
    if (t_1 <= 1d+228) then
        tmp = t_1 / (a * 2.0d0)
    else
        tmp = (x * (y / (a * 2.0d0))) - ((t / a) * (z * 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 t_1 = (x * y) - (t * (z * 9.0));
	double tmp;
	if (t_1 <= 1e+228) {
		tmp = t_1 / (a * 2.0);
	} else {
		tmp = (x * (y / (a * 2.0))) - ((t / a) * (z * 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):
	t_1 = (x * y) - (t * (z * 9.0))
	tmp = 0
	if t_1 <= 1e+228:
		tmp = t_1 / (a * 2.0)
	else:
		tmp = (x * (y / (a * 2.0))) - ((t / a) * (z * 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)
	t_1 = Float64(Float64(x * y) - Float64(t * Float64(z * 9.0)))
	tmp = 0.0
	if (t_1 <= 1e+228)
		tmp = Float64(t_1 / Float64(a * 2.0));
	else
		tmp = Float64(Float64(x * Float64(y / Float64(a * 2.0))) - Float64(Float64(t / a) * Float64(z * 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)
	t_1 = (x * y) - (t * (z * 9.0));
	tmp = 0.0;
	if (t_1 <= 1e+228)
		tmp = t_1 / (a * 2.0);
	else
		tmp = (x * (y / (a * 2.0))) - ((t / a) * (z * 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_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+228], N[(t$95$1 / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * N[(z * 4.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 9.9999999999999992e227

   1. Initial program 96.9%

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

   if 9.9999999999999992e227 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 78.7%

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

      1. div-sub 73.8%

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

      2. associate-/l* 78.4%

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

      3. associate-/l* 90.2%

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

   4. Applied egg-rr 90.2%

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

   5. Taylor expanded in z around 0 78.5%

      \[\leadsto x \cdot \frac{y}{a \cdot 2} - \color{blue}{4.5 \cdot \frac{t \cdot z}{a}} \]
   6. Step-by-step derivation

      1. *-commutative 78.5%

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

      2. associate-*l/ 90.2%

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

      3. associate-*l* 90.2%

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

   7. Simplified 90.2%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - t \cdot \left(z \cdot 9\right) \leq 10^{+228}:\\ \;\;\;\;\frac{x \cdot y - t \cdot \left(z \cdot 9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2} - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-39} \lor \neg \left(x \leq 3.8 \cdot 10^{+15}\right):\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.4e-39) (not (<= x 3.8e+15)))
   (* x (* y (/ 0.5 a)))
   (* -4.5 (/ (* z t) a))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.4e-39) || !(x <= 3.8e+15)) {
		tmp = x * (y * (0.5 / a));
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-1.4d-39)) .or. (.not. (x <= 3.8d+15))) then
        tmp = x * (y * (0.5d0 / a))
    else
        tmp = (-4.5d0) * ((z * t) / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.4e-39) || !(x <= 3.8e+15)) {
		tmp = x * (y * (0.5 / a));
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.4e-39) or not (x <= 3.8e+15):
		tmp = x * (y * (0.5 / a))
	else:
		tmp = -4.5 * ((z * t) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.4e-39) || !(x <= 3.8e+15))
		tmp = Float64(x * Float64(y * Float64(0.5 / a)));
	else
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.4e-39) || ~((x <= 3.8e+15)))
		tmp = x * (y * (0.5 / a));
	else
		tmp = -4.5 * ((z * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.4e-39], N[Not[LessEqual[x, 3.8e+15]], $MachinePrecision]], N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4000000000000001e-39 or 3.8e15 < x

   1. Initial program 92.2%

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

   3. Taylor expanded in a around 0 92.2%

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

      1. associate-*r/ 92.2%

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

      2. cancel-sign-sub-inv 92.2%

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

      3. metadata-eval 92.2%

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

      4. *-commutative 92.2%

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

      5. associate-*r* 92.2%

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

      6. fma-define 92.9%

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

      7. associate-*l/ 92.9%

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

      8. *-commutative 92.9%

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

      9. fma-define 92.2%

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

      10. +-commutative 92.2%

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

      11. fma-define 93.0%

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

   5. Simplified 93.0%

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

   6. Taylor expanded in t around 0 65.4%

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

      1. associate-*r/ 65.4%

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

      2. associate-*l/ 65.3%

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

      3. *-commutative 65.3%

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

      4. associate-*l* 63.7%

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

   8. Simplified 63.7%

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

   if -1.4000000000000001e-39 < x < 3.8e15

   1. Initial program 96.2%

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

   3. Taylor expanded in x around 0 71.8%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-39} \lor \neg \left(x \leq 3.8 \cdot 10^{+15}\right):\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \left(0.5 \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+15}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \end{array} \end{array} \]

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 (<= x -5.8e-39)
   (* x (* 0.5 (/ y a)))
   (if (<= x 1.65e+15) (* -4.5 (/ (* z t) a)) (* x (* y (/ 0.5 a))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5.8e-39) {
		tmp = x * (0.5 * (y / a));
	} else if (x <= 1.65e+15) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = x * (y * (0.5 / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-5.8d-39)) then
        tmp = x * (0.5d0 * (y / a))
    else if (x <= 1.65d+15) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = x * (y * (0.5d0 / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5.8e-39) {
		tmp = x * (0.5 * (y / a));
	} else if (x <= 1.65e+15) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = x * (y * (0.5 / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -5.8e-39:
		tmp = x * (0.5 * (y / a))
	elif x <= 1.65e+15:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = x * (y * (0.5 / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -5.8e-39)
		tmp = Float64(x * Float64(0.5 * Float64(y / a)));
	elseif (x <= 1.65e+15)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = Float64(x * Float64(y * Float64(0.5 / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -5.8e-39)
		tmp = x * (0.5 * (y / a));
	elseif (x <= 1.65e+15)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = x * (y * (0.5 / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[x, -5.8e-39], N[(x * N[(0.5 * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.65e+15], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.79999999999999975e-39

   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 inf 66.4%

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

      1. *-commutative 66.4%

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

      2. associate-/l* 65.1%

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

      3. associate-*l* 65.1%

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

   5. Simplified 65.1%

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

   if -5.79999999999999975e-39 < x < 1.65e15

   1. Initial program 96.2%

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

   3. Taylor expanded in x around 0 71.8%

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

   if 1.65e15 < x

   1. Initial program 91.0%

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

   3. Taylor expanded in a around 0 91.0%

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

      1. associate-*r/ 91.0%

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

      2. cancel-sign-sub-inv 91.0%

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

      3. metadata-eval 91.0%

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

      4. *-commutative 91.0%

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

      5. associate-*r* 91.0%

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

      6. fma-define 91.0%

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

      7. associate-*l/ 90.9%

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

      8. *-commutative 90.9%

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

      9. fma-define 90.9%

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

      10. +-commutative 90.9%

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

      11. fma-define 92.4%

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

   5. Simplified 92.4%

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

   6. Taylor expanded in t around 0 64.1%

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

      1. associate-*r/ 64.1%

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

      2. associate-*l/ 64.0%

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

      3. *-commutative 64.0%

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

      4. associate-*l* 62.1%

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

   8. Simplified 62.1%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \left(0.5 \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+15}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{2} \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+17}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \end{array} \end{array} \]

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 (<= x -1.15e-38)
   (* (/ x 2.0) (/ y a))
   (if (<= x 5e+17) (* -4.5 (/ (* z t) a)) (* x (* y (/ 0.5 a))))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.15e-38) {
		tmp = (x / 2.0) * (y / a);
	} else if (x <= 5e+17) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = x * (y * (0.5 / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.15d-38)) then
        tmp = (x / 2.0d0) * (y / a)
    else if (x <= 5d+17) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = x * (y * (0.5d0 / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.15e-38) {
		tmp = (x / 2.0) * (y / a);
	} else if (x <= 5e+17) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = x * (y * (0.5 / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.15e-38:
		tmp = (x / 2.0) * (y / a)
	elif x <= 5e+17:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = x * (y * (0.5 / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.15e-38)
		tmp = Float64(Float64(x / 2.0) * Float64(y / a));
	elseif (x <= 5e+17)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = Float64(x * Float64(y * Float64(0.5 / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.15e-38)
		tmp = (x / 2.0) * (y / a);
	elseif (x <= 5e+17)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = x * (y * (0.5 / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.15e-38], N[(N[(x / 2.0), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e+17], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.15000000000000001e-38

   1. Initial program 93.3%

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

      1. clear-num 93.2%

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

      2. inv-pow 93.2%

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

      3. *-commutative 93.2%

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

      4. associate-/l* 93.2%

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

      5. fma-neg 94.5%

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

      6. *-commutative 94.5%

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

      7. distribute-rgt-neg-in 94.5%

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

      8. distribute-rgt-neg-in 94.5%

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

      9. metadata-eval 94.5%

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

   4. Applied egg-rr 94.5%

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

      1. unpow-1 94.5%

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

      2. associate-/r* 94.5%

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

      3. metadata-eval 94.5%

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

      4. fma-define 93.2%

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

      5. +-commutative 93.2%

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

      6. fma-define 93.3%

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

   6. Simplified 93.3%

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

   7. Taylor expanded in t around 0 66.3%

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

      1. div-inv 66.3%

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

      2. clear-num 66.4%

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

      3. metadata-eval 66.4%

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

      4. times-frac 66.4%

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

      5. *-un-lft-identity 66.4%

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

      6. *-commutative 66.4%

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

      7. *-commutative 66.4%

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

      8. times-frac 65.1%

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

   9. Applied egg-rr 65.1%

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

   if -1.15000000000000001e-38 < x < 5e17

   1. Initial program 96.2%

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

   3. Taylor expanded in x around 0 71.8%

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

   if 5e17 < x

   1. Initial program 91.0%

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

   3. Taylor expanded in a around 0 91.0%

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

      1. associate-*r/ 91.0%

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

      2. cancel-sign-sub-inv 91.0%

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

      3. metadata-eval 91.0%

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

      4. *-commutative 91.0%

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

      5. associate-*r* 91.0%

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

      6. fma-define 91.0%

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

      7. associate-*l/ 90.9%

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

      8. *-commutative 90.9%

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

      9. fma-define 90.9%

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

      10. +-commutative 90.9%

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

      11. fma-define 92.4%

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

   5. Simplified 92.4%

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

   6. Taylor expanded in t around 0 64.1%

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

      1. associate-*r/ 64.1%

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

      2. associate-*l/ 64.0%

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

      3. *-commutative 64.0%

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

      4. associate-*l* 62.1%

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

   8. Simplified 62.1%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{2} \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+17}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 91.2% accurate, 1.0× speedup

Math

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

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

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 = ((x * y) - (t * (z * 9.0d0))) / (a * 2.0d0)
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 ((x * y) - (t * (z * 9.0))) / (a * 2.0);
}

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

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(Float64(Float64(x * y) - Float64(t * Float64(z * 9.0))) / Float64(a * 2.0))
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 = ((x * y) - (t * (z * 9.0))) / (a * 2.0);
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[(N[(N[(x * y), $MachinePrecision] - N[(t * N[(z * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.0%

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

3. Final simplification 94.0%

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

Alternative 13: 51.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 4.3 \cdot 10^{+79}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= y 4.3e+79) (* -4.5 (/ (* z t) a)) (* -4.5 (* z (/ t a)))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 4.3e+79) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= 4.3d+79) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = (-4.5d0) * (z * (t / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 4.3e+79) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = -4.5 * (z * (t / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if y <= 4.3e+79:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = -4.5 * (z * (t / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 4.3e+79)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = Float64(-4.5 * Float64(z * Float64(t / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 4.3e+79)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = -4.5 * (z * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[y, 4.3e+79], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.3000000000000003e79

   1. Initial program 93.5%

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

   3. Taylor expanded in x around 0 55.2%

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

   if 4.3000000000000003e79 < y

   1. Initial program 96.0%

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

   3. Taylor expanded in x around 0 30.7%

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

      1. *-commutative 30.7%

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

      2. associate-/l* 29.3%

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

   5. Applied egg-rr 29.3%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.3 \cdot 10^{+79}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.5% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.0%

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

3. Taylor expanded in x around 0 50.3%

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

   1. *-commutative 50.3%

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

   2. associate-/l* 48.4%

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

5. Applied egg-rr 48.4%

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

6. Final simplification 48.4%

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

Developer target: 93.5% 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 2024040 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

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

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