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

Percentage Accurate: 91.4% → 96.0%

Time: 9.0s

Alternatives: 8

Speedup: 0.5×

• 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: 91.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;y \cdot \left(x \cdot \left(\frac{0.5}{a} - 4.5 \cdot \left(t \cdot \frac{z}{\left(x \cdot y\right) \cdot a}\right)\right)\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+213}:\\ \;\;\;\;\frac{t\_1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2} - \left(z \cdot 9\right) \cdot \frac{t}{a \cdot 2}\\ \end{array} \end{array} \]

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) (* (* z 9.0) t))))
   (if (<= t_1 (- INFINITY))
     (* y (* x (- (/ 0.5 a) (* 4.5 (* t (/ z (* (* x y) a)))))))
     (if (<= t_1 1e+213)
       (/ t_1 (* a 2.0))
       (- (* x (/ y (* a 2.0))) (* (* 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) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y * (x * ((0.5 / a) - (4.5 * (t * (z / ((x * y) * a))))));
	} else if (t_1 <= 1e+213) {
		tmp = t_1 / (a * 2.0);
	} else {
		tmp = (x * (y / (a * 2.0))) - ((z * 9.0) * (t / (a * 2.0)));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y * (x * ((0.5 / a) - (4.5 * (t * (z / ((x * y) * a))))));
	} else if (t_1 <= 1e+213) {
		tmp = t_1 / (a * 2.0);
	} else {
		tmp = (x * (y / (a * 2.0))) - ((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) - ((z * 9.0) * t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y * (x * ((0.5 / a) - (4.5 * (t * (z / ((x * y) * a))))))
	elif t_1 <= 1e+213:
		tmp = t_1 / (a * 2.0)
	else:
		tmp = (x * (y / (a * 2.0))) - ((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(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y * Float64(x * Float64(Float64(0.5 / a) - Float64(4.5 * Float64(t * Float64(z / Float64(Float64(x * y) * a)))))));
	elseif (t_1 <= 1e+213)
		tmp = Float64(t_1 / Float64(a * 2.0));
	else
		tmp = Float64(Float64(x * Float64(y / Float64(a * 2.0))) - 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) - ((z * 9.0) * t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y * (x * ((0.5 / a) - (4.5 * (t * (z / ((x * y) * a))))));
	elseif (t_1 <= 1e+213)
		tmp = t_1 / (a * 2.0);
	else
		tmp = (x * (y / (a * 2.0))) - ((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[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y * N[(x * N[(N[(0.5 / a), $MachinePrecision] - N[(4.5 * N[(t * N[(z / N[(N[(x * y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+213], N[(t$95$1 / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * N[(t / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 71.9%

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

   3. Taylor expanded in y around inf 88.9%

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

   4. Taylor expanded in x around -inf 88.8%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(x \cdot \left(4.5 \cdot \frac{t \cdot z}{a \cdot \left(x \cdot y\right)} - 0.5 \cdot \frac{1}{a}\right)\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 88.8%

         \[\leadsto y \cdot \color{blue}{\left(\left(-1 \cdot x\right) \cdot \left(4.5 \cdot \frac{t \cdot z}{a \cdot \left(x \cdot y\right)} - 0.5 \cdot \frac{1}{a}\right)\right)} \]

      2. mul-1-neg 88.8%

         \[\leadsto y \cdot \left(\color{blue}{\left(-x\right)} \cdot \left(4.5 \cdot \frac{t \cdot z}{a \cdot \left(x \cdot y\right)} - 0.5 \cdot \frac{1}{a}\right)\right) \]

      3. associate-/l* 99.8%

         \[\leadsto y \cdot \left(\left(-x\right) \cdot \left(4.5 \cdot \color{blue}{\left(t \cdot \frac{z}{a \cdot \left(x \cdot y\right)}\right)} - 0.5 \cdot \frac{1}{a}\right)\right) \]

      4. associate-*r/ 99.8%

         \[\leadsto y \cdot \left(\left(-x\right) \cdot \left(4.5 \cdot \left(t \cdot \frac{z}{a \cdot \left(x \cdot y\right)}\right) - \color{blue}{\frac{0.5 \cdot 1}{a}}\right)\right) \]

      5. metadata-eval 99.8%

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

   6. Simplified 99.8%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t)) < 9.99999999999999984e212

   1. Initial program 99.1%

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

   if 9.99999999999999984e212 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z #s(literal 9 binary64)) t))

   1. Initial program 81.2%

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

      1. div-sub 81.2%

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

      2. associate-/l* 84.7%

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

      3. associate-/l* 96.0%

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

   4. Applied egg-rr 96.0%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty:\\ \;\;\;\;y \cdot \left(x \cdot \left(\frac{0.5}{a} - 4.5 \cdot \left(t \cdot \frac{z}{\left(x \cdot y\right) \cdot a}\right)\right)\right)\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 10^{+213}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2} - \left(z \cdot 9\right) \cdot \frac{t}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 67.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := 0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{if}\;x \leq -8.2 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-36}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-61} \lor \neg \left(x \leq 2.55 \cdot 10^{-57}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (* x (/ y a)))))
   (if (<= x -8.2e+14)
     t_1
     (if (<= x -5.4e-36)
       (* -4.5 (* t (/ z a)))
       (if (or (<= x -3.8e-61) (not (<= x 2.55e-57)))
         t_1
         (* -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 t_1 = 0.5 * (x * (y / a));
	double tmp;
	if (x <= -8.2e+14) {
		tmp = t_1;
	} else if (x <= -5.4e-36) {
		tmp = -4.5 * (t * (z / a));
	} else if ((x <= -3.8e-61) || !(x <= 2.55e-57)) {
		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.
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 * (x * (y / a))
    if (x <= (-8.2d+14)) then
        tmp = t_1
    else if (x <= (-5.4d-36)) then
        tmp = (-4.5d0) * (t * (z / a))
    else if ((x <= (-3.8d-61)) .or. (.not. (x <= 2.55d-57))) 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;
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 * (x * (y / a));
	double tmp;
	if (x <= -8.2e+14) {
		tmp = t_1;
	} else if (x <= -5.4e-36) {
		tmp = -4.5 * (t * (z / a));
	} else if ((x <= -3.8e-61) || !(x <= 2.55e-57)) {
		tmp = t_1;
	} 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):
	t_1 = 0.5 * (x * (y / a))
	tmp = 0
	if x <= -8.2e+14:
		tmp = t_1
	elif x <= -5.4e-36:
		tmp = -4.5 * (t * (z / a))
	elif (x <= -3.8e-61) or not (x <= 2.55e-57):
		tmp = t_1
	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)
	t_1 = Float64(0.5 * Float64(x * Float64(y / a)))
	tmp = 0.0
	if (x <= -8.2e+14)
		tmp = t_1;
	elseif (x <= -5.4e-36)
		tmp = Float64(-4.5 * Float64(t * Float64(z / a)));
	elseif ((x <= -3.8e-61) || !(x <= 2.55e-57))
		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])){:}
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 * (x * (y / a));
	tmp = 0.0;
	if (x <= -8.2e+14)
		tmp = t_1;
	elseif (x <= -5.4e-36)
		tmp = -4.5 * (t * (z / a));
	elseif ((x <= -3.8e-61) || ~((x <= 2.55e-57)))
		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.
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[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.2e+14], t$95$1, If[LessEqual[x, -5.4e-36], N[(-4.5 * N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -3.8e-61], N[Not[LessEqual[x, 2.55e-57]], $MachinePrecision]], t$95$1, N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.2e14 or -5.40000000000000015e-36 < x < -3.7999999999999998e-61 or 2.55e-57 < x

   1. Initial program 89.3%

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

   3. Taylor expanded in x around inf 64.6%

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

      1. associate-/l* 68.9%

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

   5. Simplified 68.9%

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

   if -8.2e14 < x < -5.40000000000000015e-36

   1. Initial program 86.4%

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

   3. Taylor expanded in x around 0 31.8%

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

      1. associate-/l* 44.7%

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

   5. Simplified 44.7%

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

   if -3.7999999999999998e-61 < x < 2.55e-57

   1. Initial program 98.6%

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

   3. Taylor expanded in x around 0 79.8%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+14}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-36}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-61} \lor \neg \left(x \leq 2.55 \cdot 10^{-57}\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+291}\right):\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \end{array} \end{array} \]

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
 (if (or (<= (* x y) (- INFINITY)) (not (<= (* x y) 5e+291)))
   (* y (* 0.5 (/ x a)))
   (/ (- (* x y) (* (* 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 tmp;
	if (((x * y) <= -((double) INFINITY)) || !((x * y) <= 5e+291)) {
		tmp = y * (0.5 * (x / a));
	} else {
		tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -Double.POSITIVE_INFINITY) || !((x * y) <= 5e+291)) {
		tmp = y * (0.5 * (x / a));
	} else {
		tmp = ((x * y) - ((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):
	tmp = 0
	if ((x * y) <= -math.inf) or not ((x * y) <= 5e+291):
		tmp = y * (0.5 * (x / a))
	else:
		tmp = ((x * y) - ((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)
	tmp = 0.0
	if ((Float64(x * y) <= Float64(-Inf)) || !(Float64(x * y) <= 5e+291))
		tmp = Float64(y * Float64(0.5 * Float64(x / a)));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * 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)
	tmp = 0.0;
	if (((x * y) <= -Inf) || ~(((x * y) <= 5e+291)))
		tmp = y * (0.5 * (x / a));
	else
		tmp = ((x * y) - ((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_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e+291]], $MachinePrecision]], N[(y * N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -inf.0 or 5.0000000000000001e291 < (*.f64 x y)

   1. Initial program 70.4%

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

   3. Taylor expanded in y around inf 89.3%

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

   4. Taylor expanded in t around 0 98.9%

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

   if -inf.0 < (*.f64 x y) < 5.0000000000000001e291

   1. Initial program 97.0%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty \lor \neg \left(x \cdot y \leq 5 \cdot 10^{+291}\right):\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 4 \cdot 10^{+60}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2} - \left(z \cdot 9\right) \cdot \frac{t}{a \cdot 2}\\ \end{array} \end{array} \]

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
 (if (<= (* a 2.0) 4e+60)
   (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0))
   (- (* x (/ y (* a 2.0))) (* (* 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 tmp;
	if ((a * 2.0) <= 4e+60) {
		tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
	} else {
		tmp = (x * (y / (a * 2.0))) - ((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) :: tmp
    if ((a * 2.0d0) <= 4d+60) then
        tmp = ((x * y) - ((z * 9.0d0) * t)) / (a * 2.0d0)
    else
        tmp = (x * (y / (a * 2.0d0))) - ((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 tmp;
	if ((a * 2.0) <= 4e+60) {
		tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
	} else {
		tmp = (x * (y / (a * 2.0))) - ((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):
	tmp = 0
	if (a * 2.0) <= 4e+60:
		tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0)
	else:
		tmp = (x * (y / (a * 2.0))) - ((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)
	tmp = 0.0
	if (Float64(a * 2.0) <= 4e+60)
		tmp = Float64(Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t)) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(x * Float64(y / Float64(a * 2.0))) - 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)
	tmp = 0.0;
	if ((a * 2.0) <= 4e+60)
		tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
	else
		tmp = (x * (y / (a * 2.0))) - ((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_] := If[LessEqual[N[(a * 2.0), $MachinePrecision], 4e+60], N[(N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y / N[(a * 2.0), $MachinePrecision]), $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 a #s(literal 2 binary64)) < 3.9999999999999998e60

   1. Initial program 96.1%

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

   if 3.9999999999999998e60 < (*.f64 a #s(literal 2 binary64))

   1. Initial program 78.9%

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

      1. div-sub 78.9%

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

      2. associate-/l* 88.3%

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

      3. associate-/l* 92.6%

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

   4. Applied egg-rr 92.6%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 2 \leq 4 \cdot 10^{+60}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a \cdot 2} - \left(z \cdot 9\right) \cdot \frac{t}{a \cdot 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+68} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{-94}\right):\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* x y) -5e+68) (not (<= (* x y) 5e-94)))
   (* y (* 0.5 (/ x 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 * y) <= -5e+68) || !((x * y) <= 5e-94)) {
		tmp = y * (0.5 * (x / a));
	} else {
		tmp = -4.5 * ((z * t) / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((x * y) <= (-5d+68)) .or. (.not. ((x * y) <= 5d-94))) then
        tmp = y * (0.5d0 * (x / a))
    else
        tmp = (-4.5d0) * ((z * t) / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -5e+68) || !((x * y) <= 5e-94)) {
		tmp = y * (0.5 * (x / 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 * y) <= -5e+68) or not ((x * y) <= 5e-94):
		tmp = y * (0.5 * (x / 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 ((Float64(x * y) <= -5e+68) || !(Float64(x * y) <= 5e-94))
		tmp = Float64(y * Float64(0.5 * Float64(x / a)));
	else
		tmp = Float64(-4.5 * Float64(Float64(z * t) / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x * y) <= -5e+68) || ~(((x * y) <= 5e-94)))
		tmp = y * (0.5 * (x / a));
	else
		tmp = -4.5 * ((z * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -5e+68], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e-94]], $MachinePrecision]], N[(y * N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-4.5 * N[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -5.0000000000000004e68 or 4.9999999999999995e-94 < (*.f64 x y)

   1. Initial program 89.4%

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

   3. Taylor expanded in y around inf 84.0%

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

   4. Taylor expanded in t around 0 78.7%

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

   if -5.0000000000000004e68 < (*.f64 x y) < 4.9999999999999995e-94

   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 80.3%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+68} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{-94}\right):\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+68} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{-94}\right):\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-4.5}{a} \cdot \left(z \cdot t\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* x y) -5e+68) (not (<= (* x y) 5e-94)))
   (* y (* 0.5 (/ x a)))
   (* (/ -4.5 a) (* z t))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -5e+68) || !((x * y) <= 5e-94)) {
		tmp = y * (0.5 * (x / a));
	} else {
		tmp = (-4.5 / a) * (z * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((x * y) <= (-5d+68)) .or. (.not. ((x * y) <= 5d-94))) then
        tmp = y * (0.5d0 * (x / a))
    else
        tmp = ((-4.5d0) / a) * (z * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) <= -5e+68) || !((x * y) <= 5e-94)) {
		tmp = y * (0.5 * (x / a));
	} else {
		tmp = (-4.5 / a) * (z * t);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if ((x * y) <= -5e+68) or not ((x * y) <= 5e-94):
		tmp = y * (0.5 * (x / a))
	else:
		tmp = (-4.5 / a) * (z * t)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(x * y) <= -5e+68) || !(Float64(x * y) <= 5e-94))
		tmp = Float64(y * Float64(0.5 * Float64(x / a)));
	else
		tmp = Float64(Float64(-4.5 / a) * Float64(z * t));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x * y) <= -5e+68) || ~(((x * y) <= 5e-94)))
		tmp = y * (0.5 * (x / a));
	else
		tmp = (-4.5 / a) * (z * t);
	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[N[(x * y), $MachinePrecision], -5e+68], N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e-94]], $MachinePrecision]], N[(y * N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-4.5 / a), $MachinePrecision] * N[(z * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -5.0000000000000004e68 or 4.9999999999999995e-94 < (*.f64 x y)

   1. Initial program 89.4%

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

   3. Taylor expanded in y around inf 84.0%

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

   4. Taylor expanded in t around 0 78.7%

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

   if -5.0000000000000004e68 < (*.f64 x y) < 4.9999999999999995e-94

   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 80.3%

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

      1. associate-/l* 76.0%

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

   5. Simplified 76.0%

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

      1. *-commutative 76.0%

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

      2. associate-*r/ 80.3%

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

      3. metadata-eval 80.3%

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

      4. times-frac 79.6%

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

      5. *-commutative 79.6%

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

      6. associate-*r* 79.6%

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

      7. clear-num 79.6%

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

      8. associate-*r* 79.5%

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

      9. *-commutative 79.5%

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

      10. times-frac 80.2%

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

      11. metadata-eval 80.2%

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

   7. Applied egg-rr 80.2%

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

      1. *-commutative 80.2%

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

      2. associate-/r* 80.3%

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

      3. metadata-eval 80.3%

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

      4. *-commutative 80.3%

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

      5. associate-/r* 75.2%

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

   9. Simplified 75.2%

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

       1. associate-/l/ 80.3%

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

       2. associate-/r/ 80.3%

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

   11. Applied egg-rr 80.3%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+68} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{-94}\right):\\ \;\;\;\;y \cdot \left(0.5 \cdot \frac{x}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-4.5}{a} \cdot \left(z \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.3% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.7%

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

3. Taylor expanded in x around 0 54.8%

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

   1. associate-/l* 52.7%

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

5. Simplified 52.7%

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

6. Final simplification 52.7%

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

Alternative 8: 50.6% accurate, 1.9× speedup

Math

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

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 (* -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(Float64(z * 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[(N[(z * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 92.7%

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

3. Taylor expanded in x around 0 54.8%

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

4. Final simplification 54.8%

   \[\leadsto -4.5 \cdot \frac{z \cdot t}{a} \]
5. 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 2024059 
(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)))