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

Percentage Accurate: 91.7% → 93.0%

Time: 8.6s

Alternatives: 9

Speedup: 0.6×

• 28.5% 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: 91.7% 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: 93.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+128}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4.5, \frac{z}{a}, 0.5 \cdot \left(x \cdot \frac{y}{t \cdot a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - t\_1}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 -5e+128)
     (* t (fma -4.5 (/ z a) (* 0.5 (* x (/ y (* t a))))))
     (/ (- (* x y) t_1) (* a 2.0)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -5e+128) {
		tmp = t * fma(-4.5, (z / a), (0.5 * (x * (y / (t * a)))));
	} else {
		tmp = ((x * y) - t_1) / (a * 2.0);
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if (t_1 <= -5e+128)
		tmp = Float64(t * fma(-4.5, Float64(z / a), Float64(0.5 * Float64(x * Float64(y / Float64(t * a))))));
	else
		tmp = Float64(Float64(Float64(x * y) - t_1) / Float64(a * 2.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+128], N[(t * N[(-4.5 * N[(z / a), $MachinePrecision] + N[(0.5 * N[(x * N[(y / N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 z #s(literal 9 binary64)) t) < -5e128

   1. Initial program 77.6%

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

   3. Taylor expanded in t around inf 85.0%

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

      1. fma-define 85.0%

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

      2. associate-/l* 92.5%

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

      3. *-commutative 92.5%

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

   5. Simplified 92.5%

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

   if -5e128 < (*.f64 (*.f64 z #s(literal 9 binary64)) t)

   1. Initial program 95.3%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -5 \cdot 10^{+128}:\\ \;\;\;\;t \cdot \mathsf{fma}\left(-4.5, \frac{z}{a}, 0.5 \cdot \left(x \cdot \frac{y}{t \cdot a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 70.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := -4.5 \cdot \frac{z \cdot t}{a}\\ t_2 := y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-208}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 0.001:\\ \;\;\;\;x \cdot \frac{0.5 \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -4.5 (/ (* z t) a))) (t_2 (* y (* 0.5 (/ x a)))))
   (if (<= (* x y) -1e+29)
     t_2
     (if (<= (* x y) 5e-208)
       t_1
       (if (<= (* x y) 0.001)
         (* x (/ (* 0.5 y) a))
         (if (<= (* x y) 2e+47) t_1 t_2))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = -4.5 * ((z * t) / a);
	double t_2 = y * (0.5 * (x / a));
	double tmp;
	if ((x * y) <= -1e+29) {
		tmp = t_2;
	} else if ((x * y) <= 5e-208) {
		tmp = t_1;
	} else if ((x * y) <= 0.001) {
		tmp = x * ((0.5 * y) / a);
	} else if ((x * y) <= 2e+47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (-4.5d0) * ((z * t) / a)
    t_2 = y * (0.5d0 * (x / a))
    if ((x * y) <= (-1d+29)) then
        tmp = t_2
    else if ((x * y) <= 5d-208) then
        tmp = t_1
    else if ((x * y) <= 0.001d0) then
        tmp = x * ((0.5d0 * y) / a)
    else if ((x * y) <= 2d+47) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -4.5 * ((z * t) / a);
	double t_2 = y * (0.5 * (x / a));
	double tmp;
	if ((x * y) <= -1e+29) {
		tmp = t_2;
	} else if ((x * y) <= 5e-208) {
		tmp = t_1;
	} else if ((x * y) <= 0.001) {
		tmp = x * ((0.5 * y) / a);
	} else if ((x * y) <= 2e+47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = -4.5 * ((z * t) / a)
	t_2 = y * (0.5 * (x / a))
	tmp = 0
	if (x * y) <= -1e+29:
		tmp = t_2
	elif (x * y) <= 5e-208:
		tmp = t_1
	elif (x * y) <= 0.001:
		tmp = x * ((0.5 * y) / a)
	elif (x * y) <= 2e+47:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(-4.5 * Float64(Float64(z * t) / a))
	t_2 = Float64(y * Float64(0.5 * Float64(x / a)))
	tmp = 0.0
	if (Float64(x * y) <= -1e+29)
		tmp = t_2;
	elseif (Float64(x * y) <= 5e-208)
		tmp = t_1;
	elseif (Float64(x * y) <= 0.001)
		tmp = Float64(x * Float64(Float64(0.5 * y) / a));
	elseif (Float64(x * y) <= 2e+47)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = -4.5 * ((z * t) / a);
	t_2 = y * (0.5 * (x / a));
	tmp = 0.0;
	if ((x * y) <= -1e+29)
		tmp = t_2;
	elseif ((x * y) <= 5e-208)
		tmp = t_1;
	elseif ((x * y) <= 0.001)
		tmp = x * ((0.5 * y) / a);
	elseif ((x * y) <= 2e+47)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+29], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 5e-208], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 0.001], N[(x * N[(N[(0.5 * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+47], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -9.99999999999999914e28 or 2.0000000000000001e47 < (*.f64 x y)

   1. Initial program 86.6%

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

   3. Taylor expanded in y around inf 90.4%

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

   4. Taylor expanded in t around 0 82.7%

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

   if -9.99999999999999914e28 < (*.f64 x y) < 4.99999999999999963e-208 or 1e-3 < (*.f64 x y) < 2.0000000000000001e47

   1. Initial program 96.7%

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

   3. Taylor expanded in x around 0 79.5%

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

   if 4.99999999999999963e-208 < (*.f64 x y) < 1e-3

   1. Initial program 93.8%

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

   3. Taylor expanded in x around inf 63.8%

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

      1. *-commutative 63.8%

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

      2. associate-/l* 63.7%

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

      3. associate-*r* 63.7%

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

      4. *-commutative 63.7%

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

      5. associate-*r/ 63.7%

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

   5. Simplified 63.7%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-208}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y \leq 0.001:\\ \;\;\;\;x \cdot \frac{0.5 \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+47}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-208}:\\ \;\;\;\;\frac{z \cdot t}{a \cdot -0.2222222222222222}\\ \mathbf{elif}\;x \cdot y \leq 0.001:\\ \;\;\;\;x \cdot \frac{0.5 \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+47}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (* 0.5 (/ x a)))))
   (if (<= (* x y) -1e+29)
     t_1
     (if (<= (* x y) 5e-208)
       (/ (* z t) (* a -0.2222222222222222))
       (if (<= (* x y) 0.001)
         (* x (/ (* 0.5 y) a))
         (if (<= (* x y) 2e+47) (* -4.5 (/ (* z t) a)) t_1))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (0.5 * (x / a));
	double tmp;
	if ((x * y) <= -1e+29) {
		tmp = t_1;
	} else if ((x * y) <= 5e-208) {
		tmp = (z * t) / (a * -0.2222222222222222);
	} else if ((x * y) <= 0.001) {
		tmp = x * ((0.5 * y) / a);
	} else if ((x * y) <= 2e+47) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (0.5d0 * (x / a))
    if ((x * y) <= (-1d+29)) then
        tmp = t_1
    else if ((x * y) <= 5d-208) then
        tmp = (z * t) / (a * (-0.2222222222222222d0))
    else if ((x * y) <= 0.001d0) then
        tmp = x * ((0.5d0 * y) / a)
    else if ((x * y) <= 2d+47) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (0.5 * (x / a));
	double tmp;
	if ((x * y) <= -1e+29) {
		tmp = t_1;
	} else if ((x * y) <= 5e-208) {
		tmp = (z * t) / (a * -0.2222222222222222);
	} else if ((x * y) <= 0.001) {
		tmp = x * ((0.5 * y) / a);
	} else if ((x * y) <= 2e+47) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = y * (0.5 * (x / a))
	tmp = 0
	if (x * y) <= -1e+29:
		tmp = t_1
	elif (x * y) <= 5e-208:
		tmp = (z * t) / (a * -0.2222222222222222)
	elif (x * y) <= 0.001:
		tmp = x * ((0.5 * y) / a)
	elif (x * y) <= 2e+47:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(0.5 * Float64(x / a)))
	tmp = 0.0
	if (Float64(x * y) <= -1e+29)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-208)
		tmp = Float64(Float64(z * t) / Float64(a * -0.2222222222222222));
	elseif (Float64(x * y) <= 0.001)
		tmp = Float64(x * Float64(Float64(0.5 * y) / a));
	elseif (Float64(x * y) <= 2e+47)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (0.5 * (x / a));
	tmp = 0.0;
	if ((x * y) <= -1e+29)
		tmp = t_1;
	elseif ((x * y) <= 5e-208)
		tmp = (z * t) / (a * -0.2222222222222222);
	elseif ((x * y) <= 0.001)
		tmp = x * ((0.5 * y) / a);
	elseif ((x * y) <= 2e+47)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -1e+29], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-208], N[(N[(z * t), $MachinePrecision] / N[(a * -0.2222222222222222), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 0.001], N[(x * N[(N[(0.5 * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+47], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -9.99999999999999914e28 or 2.0000000000000001e47 < (*.f64 x y)

   1. Initial program 86.6%

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

   3. Taylor expanded in y around inf 90.4%

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

   4. Taylor expanded in t around 0 82.7%

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

   if -9.99999999999999914e28 < (*.f64 x y) < 4.99999999999999963e-208

   1. Initial program 96.3%

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

   3. Taylor expanded in x around 0 81.2%

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

      1. metadata-eval 81.2%

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

      2. times-frac 81.3%

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

      3. *-un-lft-identity 81.3%

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

      4. *-commutative 81.3%

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

      5. *-commutative 81.3%

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

   5. Applied egg-rr 81.3%

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

   if 4.99999999999999963e-208 < (*.f64 x y) < 1e-3

   1. Initial program 93.8%

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

   3. Taylor expanded in x around inf 63.8%

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

      1. *-commutative 63.8%

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

      2. associate-/l* 63.7%

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

      3. associate-*r* 63.7%

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

      4. *-commutative 63.7%

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

      5. associate-*r/ 63.7%

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

   5. Simplified 63.7%

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

   if 1e-3 < (*.f64 x y) < 2.0000000000000001e47

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0 64.6%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-208}:\\ \;\;\;\;\frac{z \cdot t}{a \cdot -0.2222222222222222}\\ \mathbf{elif}\;x \cdot y \leq 0.001:\\ \;\;\;\;x \cdot \frac{0.5 \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+47}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-208}:\\ \;\;\;\;\frac{z \cdot t}{a \cdot -0.2222222222222222}\\ \mathbf{elif}\;x \cdot y \leq 0.001:\\ \;\;\;\;x \cdot \frac{0.5 \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+47}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{\frac{a}{x}}}{2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -1e+29)
   (* y (* 0.5 (/ x a)))
   (if (<= (* x y) 5e-208)
     (/ (* z t) (* a -0.2222222222222222))
     (if (<= (* x y) 0.001)
       (* x (/ (* 0.5 y) a))
       (if (<= (* x y) 2e+47) (* -4.5 (/ (* z t) a)) (/ (/ y (/ a x)) 2.0))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -1e+29) {
		tmp = y * (0.5 * (x / a));
	} else if ((x * y) <= 5e-208) {
		tmp = (z * t) / (a * -0.2222222222222222);
	} else if ((x * y) <= 0.001) {
		tmp = x * ((0.5 * y) / a);
	} else if ((x * y) <= 2e+47) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = (y / (a / x)) / 2.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-1d+29)) then
        tmp = y * (0.5d0 * (x / a))
    else if ((x * y) <= 5d-208) then
        tmp = (z * t) / (a * (-0.2222222222222222d0))
    else if ((x * y) <= 0.001d0) then
        tmp = x * ((0.5d0 * y) / a)
    else if ((x * y) <= 2d+47) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = (y / (a / x)) / 2.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -1e+29) {
		tmp = y * (0.5 * (x / a));
	} else if ((x * y) <= 5e-208) {
		tmp = (z * t) / (a * -0.2222222222222222);
	} else if ((x * y) <= 0.001) {
		tmp = x * ((0.5 * y) / a);
	} else if ((x * y) <= 2e+47) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = (y / (a / x)) / 2.0;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -1e+29:
		tmp = y * (0.5 * (x / a))
	elif (x * y) <= 5e-208:
		tmp = (z * t) / (a * -0.2222222222222222)
	elif (x * y) <= 0.001:
		tmp = x * ((0.5 * y) / a)
	elif (x * y) <= 2e+47:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = (y / (a / x)) / 2.0
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -1e+29)
		tmp = Float64(y * Float64(0.5 * Float64(x / a)));
	elseif (Float64(x * y) <= 5e-208)
		tmp = Float64(Float64(z * t) / Float64(a * -0.2222222222222222));
	elseif (Float64(x * y) <= 0.001)
		tmp = Float64(x * Float64(Float64(0.5 * y) / a));
	elseif (Float64(x * y) <= 2e+47)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = Float64(Float64(y / Float64(a / x)) / 2.0);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -1e+29)
		tmp = y * (0.5 * (x / a));
	elseif ((x * y) <= 5e-208)
		tmp = (z * t) / (a * -0.2222222222222222);
	elseif ((x * y) <= 0.001)
		tmp = x * ((0.5 * y) / a);
	elseif ((x * y) <= 2e+47)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = (y / (a / x)) / 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.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -1e+29], N[(y * N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-208], N[(N[(z * t), $MachinePrecision] / N[(a * -0.2222222222222222), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 0.001], N[(x * N[(N[(0.5 * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+47], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -9.99999999999999914e28

   1. Initial program 88.7%

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

   3. Taylor expanded in y around inf 96.4%

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

   4. Taylor expanded in t around 0 86.6%

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

   if -9.99999999999999914e28 < (*.f64 x y) < 4.99999999999999963e-208

   1. Initial program 96.3%

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

   3. Taylor expanded in x around 0 81.2%

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

      1. metadata-eval 81.2%

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

      2. times-frac 81.3%

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

      3. *-un-lft-identity 81.3%

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

      4. *-commutative 81.3%

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

      5. *-commutative 81.3%

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

   5. Applied egg-rr 81.3%

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

   if 4.99999999999999963e-208 < (*.f64 x y) < 1e-3

   1. Initial program 93.8%

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

   3. Taylor expanded in x around inf 63.8%

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

      1. *-commutative 63.8%

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

      2. associate-/l* 63.7%

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

      3. associate-*r* 63.7%

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

      4. *-commutative 63.7%

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

      5. associate-*r/ 63.7%

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

   5. Simplified 63.7%

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

   if 1e-3 < (*.f64 x y) < 2.0000000000000001e47

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0 64.6%

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

   if 2.0000000000000001e47 < (*.f64 x y)

   1. Initial program 84.4%

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

      1. div-inv 84.3%

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

      2. fmm-def 84.3%

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

      3. *-commutative 84.3%

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

      4. distribute-rgt-neg-in 84.3%

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

      5. distribute-rgt-neg-in 84.3%

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

      6. metadata-eval 84.3%

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

      7. *-commutative 84.3%

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

      8. associate-/r* 84.3%

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

      9. metadata-eval 84.3%

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

   4. Applied egg-rr 84.3%

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

   5. Taylor expanded in x around inf 76.8%

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

      1. associate-*r/ 76.8%

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

      2. associate-*l* 76.8%

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

      3. metadata-eval 76.8%

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

      4. div-inv 76.8%

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

      5. associate-*l/ 78.5%

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

      6. associate-*r/ 78.5%

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

   7. Applied egg-rr 78.5%

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

   8. Taylor expanded in x around 0 76.8%

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

      1. associate-*r/ 75.2%

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

      2. *-commutative 75.2%

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

      3. associate-/r/ 78.4%

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

   10. Simplified 78.4%

       \[\leadsto \frac{\color{blue}{\frac{y}{\frac{a}{x}}}}{2} \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-208}:\\ \;\;\;\;\frac{z \cdot t}{a \cdot -0.2222222222222222}\\ \mathbf{elif}\;x \cdot y \leq 0.001:\\ \;\;\;\;x \cdot \frac{0.5 \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+47}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{\frac{a}{x}}}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot \frac{0.5 \cdot y}{a}\\ \mathbf{if}\;y \leq -0.4:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-91}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-118} \lor \neg \left(y \leq 6 \cdot 10^{-67}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ (* 0.5 y) a))))
   (if (<= y -0.4)
     t_1
     (if (<= y -3.5e-91)
       (* -4.5 (* t (/ z a)))
       (if (or (<= y -5.1e-118) (not (<= y 6e-67)))
         t_1
         (* -4.5 (/ (* z t) a)))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((0.5 * y) / a);
	double tmp;
	if (y <= -0.4) {
		tmp = t_1;
	} else if (y <= -3.5e-91) {
		tmp = -4.5 * (t * (z / a));
	} else if ((y <= -5.1e-118) || !(y <= 6e-67)) {
		tmp = t_1;
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((0.5d0 * y) / a)
    if (y <= (-0.4d0)) then
        tmp = t_1
    else if (y <= (-3.5d-91)) then
        tmp = (-4.5d0) * (t * (z / a))
    else if ((y <= (-5.1d-118)) .or. (.not. (y <= 6d-67))) then
        tmp = t_1
    else
        tmp = (-4.5d0) * ((z * t) / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((0.5 * y) / a);
	double tmp;
	if (y <= -0.4) {
		tmp = t_1;
	} else if (y <= -3.5e-91) {
		tmp = -4.5 * (t * (z / a));
	} else if ((y <= -5.1e-118) || !(y <= 6e-67)) {
		tmp = t_1;
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = x * ((0.5 * y) / a)
	tmp = 0
	if y <= -0.4:
		tmp = t_1
	elif y <= -3.5e-91:
		tmp = -4.5 * (t * (z / a))
	elif (y <= -5.1e-118) or not (y <= 6e-67):
		tmp = t_1
	else:
		tmp = -4.5 * ((z * t) / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(0.5 * y) / a))
	tmp = 0.0
	if (y <= -0.4)
		tmp = t_1;
	elseif (y <= -3.5e-91)
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	elseif ((y <= -5.1e-118) || !(y <= 6e-67))
		tmp = t_1;
	else
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((0.5 * y) / a);
	tmp = 0.0;
	if (y <= -0.4)
		tmp = t_1;
	elseif (y <= -3.5e-91)
		tmp = -4.5 * (t * (z / a));
	elseif ((y <= -5.1e-118) || ~((y <= 6e-67)))
		tmp = t_1;
	else
		tmp = -4.5 * ((z * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(0.5 * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.4], t$95$1, If[LessEqual[y, -3.5e-91], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -5.1e-118], N[Not[LessEqual[y, 6e-67]], $MachinePrecision]], t$95$1, N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.40000000000000002 or -3.4999999999999999e-91 < y < -5.09999999999999964e-118 or 6.00000000000000065e-67 < y

   1. Initial program 90.0%

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

   3. Taylor expanded in x around inf 65.2%

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

      1. *-commutative 65.2%

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

      2. associate-/l* 65.8%

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

      3. associate-*r* 65.8%

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

      4. *-commutative 65.8%

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

      5. associate-*r/ 65.8%

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

   5. Simplified 65.8%

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

   if -0.40000000000000002 < y < -3.4999999999999999e-91

   1. Initial program 87.7%

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

   3. Taylor expanded in x around 0 48.8%

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

      1. associate-/l* 60.8%

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

   5. Simplified 60.8%

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

   if -5.09999999999999964e-118 < y < 6.00000000000000065e-67

   1. Initial program 95.3%

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

   3. Taylor expanded in x around 0 69.2%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.4:\\ \;\;\;\;x \cdot \frac{0.5 \cdot y}{a}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-91}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-118} \lor \neg \left(y \leq 6 \cdot 10^{-67}\right):\\ \;\;\;\;x \cdot \frac{0.5 \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{z}{-0.2222222222222222} \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - t\_1}{a \cdot 2}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (* z 9.0) t)))
   (if (<= t_1 (- INFINITY))
     (* (/ z -0.2222222222222222) (/ t a))
     (/ (- (* x y) t_1) (* a 2.0)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (z / -0.2222222222222222) * (t / a);
	} else {
		tmp = ((x * y) - t_1) / (a * 2.0);
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * 9.0) * t;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (z / -0.2222222222222222) * (t / a);
	} else {
		tmp = ((x * y) - t_1) / (a * 2.0);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (z * 9.0) * t
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (z / -0.2222222222222222) * (t / a)
	else:
		tmp = ((x * y) - t_1) / (a * 2.0)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * 9.0) * t)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(z / -0.2222222222222222) * Float64(t / a));
	else
		tmp = Float64(Float64(Float64(x * y) - t_1) / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * 9.0) * t;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (z / -0.2222222222222222) * (t / a);
	else
		tmp = ((x * y) - t_1) / (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.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(z / -0.2222222222222222), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - t$95$1), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 63.8%

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

   3. Taylor expanded in x around 0 64.3%

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

      1. associate-/l* 94.9%

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

   5. Simplified 94.9%

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

      1. *-commutative 94.9%

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

      2. associate-*r/ 64.3%

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

      3. metadata-eval 64.3%

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

      4. times-frac 64.3%

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

      5. *-commutative 64.3%

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

      6. associate-*r* 64.3%

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

      7. clear-num 64.3%

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

      8. associate-*r* 64.3%

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

      9. *-commutative 64.3%

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

      10. times-frac 64.3%

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

      11. metadata-eval 64.3%

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

   7. Applied egg-rr 64.3%

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

      1. associate-*l/ 64.3%

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

   9. Simplified 64.3%

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

       1. clear-num 64.3%

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

       2. *-commutative 64.3%

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

       3. *-commutative 64.3%

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

       4. times-frac 95.1%

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

   11. Applied egg-rr 95.1%

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

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

   1. Initial program 94.3%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot 9\right) \cdot t \leq -\infty:\\ \;\;\;\;\frac{z}{-0.2222222222222222} \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.4% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -Inf)
		tmp = y * (0.5 * (x / a));
	else
		tmp = ((x * y) + (t * (z * -9.0))) * (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.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(y * N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] + N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 58.1%

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

   3. Taylor expanded in y around inf 93.4%

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

   4. Taylor expanded in t around 0 93.4%

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

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

   1. Initial program 94.0%

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

      1. div-inv 94.0%

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

      2. fmm-def 93.9%

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

      3. *-commutative 93.9%

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

      4. distribute-rgt-neg-in 93.9%

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

      5. distribute-rgt-neg-in 93.9%

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

      6. metadata-eval 93.9%

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

      7. *-commutative 93.9%

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

      8. associate-/r* 93.9%

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

      9. metadata-eval 93.9%

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

   4. Applied egg-rr 93.9%

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

      1. fma-undefine 94.0%

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

   6. Applied egg-rr 94.0%

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

4. Final simplification 93.9%

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

Alternative 8: 51.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 4.7 \cdot 10^{+190}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= t 4.7e+190) (* -4.5 (/ (* z t) a)) (* -4.5 (* t (/ z a)))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 4.7e+190) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = -4.5 * (t * (z / a));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= 4.7d+190) then
        tmp = (-4.5d0) * ((z * t) / a)
    else
        tmp = (-4.5d0) * (t * (z / a))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 4.7e+190) {
		tmp = -4.5 * ((z * t) / a);
	} else {
		tmp = -4.5 * (t * (z / a));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if t <= 4.7e+190:
		tmp = -4.5 * ((z * t) / a)
	else:
		tmp = -4.5 * (t * (z / a))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 4.7e+190)
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	else
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 4.7e+190)
		tmp = -4.5 * ((z * t) / a);
	else
		tmp = -4.5 * (t * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[t, 4.7e+190], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 4.6999999999999998e190

   1. Initial program 92.8%

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

   3. Taylor expanded in x around 0 46.5%

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

   if 4.6999999999999998e190 < t

   1. Initial program 83.6%

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

   3. Taylor expanded in x around 0 60.3%

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

      1. associate-/l* 69.7%

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

   5. Simplified 69.7%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 4.7 \cdot 10^{+190}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.3% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.8%

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

3. Taylor expanded in x around 0 48.0%

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

   1. associate-/l* 50.6%

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

5. Simplified 50.6%

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

6. Final simplification 50.6%

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

Developer target: 93.9% 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 2024095 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

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

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